PJ^\t/^^/^^^r^^^«/5^t'^\^«^t/i^^?^'^^I/^•t/rvt/5^I/i\t/F^5^^^ 


OUR   OWN 


PRIMARY  ARITHMETIC. 


I 


BY 


KEV.  S.  LANDER,  A.  M., 

TRINCIPAL  or  LINCOLNTON  FEMALE   8EMINARY. 


SECOND    EDITION, 


GRElfiNSBORO,  N.  C: 
PUBLISHBD  BY  STERLING,  CAMPBELL  AMD  ILBRIQHT 

RICHMOND,  TA.:  W.  HARQRAVl  IVHITl. 
CX)L\JMBI1,  8.  C:  TOWNSIMD  AND  KOKTU . 


^//J\^^^t'l^^^l'W^^t''•  ^^sv^^l4^4•  J^l^>t^^^^'Tvl?^i4^t/^^  ^ 


>''' 


- 

George  Washington  Flowers 

Memorial  Collection 

1 

DUKE  UNIVERSITY  LIBRARY 

ESTABLISHED  BV  THE 

FAMILY  OF 

COLONEL   FLOWERS 

^£^-..7)^  V 


OUR    OTV'N^ 


PRIMARY  ARITHMETIC. 


BY 

REV.  S.  LANDER,  A.  M., 

PRINCIPAL   OF   LINCOLNTON   FEMALE   SEMINARY. 


-«d»- 


SECOND   EDITION, 


GRESNSBOflO,  N.  C: 
PUBLISHED  BY  STERLING,  CAMPBELL  AND  ALBRIGHT 

RICHMOND,  TA.:  W.  HARGllAVlJ  WHITE. 
COLUMBIA,  S.  Q^  TOWNSEND  AND  NORTH. 


PREFACE. 

The  following  pages  are  respectfully  offered  as  an  intro- 
duction to  the  author's  School  Arithmetic,  in  the  h(jpe  that 
they  may  in  some  sort  supply  a  necessity  which,  has  long 
been  felt  to  exist. 


Entered  according  to  Act  of  Congress,  in  the  year  1863, 

BY  REV.  S.  LANDER, 
In  the   Clerk's  Office  of  the  District  Court  of  the^Con 
federate  States,  for  the  District  of  Cape  Fear,        '/ 
North  Carolina. 


'P. 
J. 


PEIMARY  ARITHMETIC. 


-^♦^ 


PART 


-••#- 


ADDITION. 

§  1.     One  and  one  are  how  many  ? 

+  +  ++  . 

One  and  two  are  how  many  1 

+  ++  +++ 

One  and  three  are  how  many  ? 

+  +++      ++++ 

One  and  four  are  how  many  % 
One  and  five  are  how  many  ? 
One  and  six  are  how  manjt  ?  , 

One  and  seven  are  how  many  ? 
One  and  eight  are  how  many  ? 
One  and  nine  are  how  many  1 
1.  John  gave  one  cent  for  a  slate  pencil,  and  five  cents 
for  a  lead  pencil ;  what  did  he  give  for  them  both  ? 

Model. — One  and  five  are  six ;  hence,  he  gave  six  cents 
for  them  both.    • 
3 


§2  PRIMA&Y   ARITHMETIC. 

• 

2.  Willie  bought  an  apple  for  one  cent,  and  some  candy 
for  four  cents ;  what  did  they  both  cost  him  ? 

3.  Mary  gave  one  peach  to  Lizzie,  and  two  to  Emma ; 
how  many  did  she  give  to  them  both? 

4.  A  man  gave  one  dollar  for  a  pocket  knife,  and  eight 
dollars  for  a  vest^  what  did  he  give  for  both  ? 

5.  Father  sowed  one  acre  in  turnips,  and  nine  acres  in 
oats ;  how  many  acres  did  he  sow  in  both  ? 

6.  Mother  gave  Lucy  one  biscuit  before  dinner,  and  one 
before  supper  ;  how  many  did  she  give  her  both  times  ? 

7.  James  walked  one  mile  in  the  ni'  '.-ning,  and  two  miles 
in  the  afternoon  ;  how  far  did  he  wall;  i  /I  day  ? 

8.  If  a  pencil  cost  one  cent;  and  a  shite  cost  six  cents, 
what  do  both  together  cost  ? 


§  2.     Two  and  one  are  how  many  ? 

++  +  +++ - 

Two  and  two  are  how  many  ? 

-f+  ++        +  +  +  -)-  .        . 

Two  and  three  are  how  many  ? 
Two  and  four  .are  how  many  1 
Two  and  five  are  how  many  ? 
Two  and  six  are  how  many  ? 
Two  and  seven  are  how  many  ? 
Two  and  eight  are  how  many  ? 
'    Two  and  nine  are  how  many  ? 

1.  Susan  gave  two  cents  to  one  beggar,  and  one  to  an 
other ;  how  many  did  she  give  to  both  ? 

Model. — Two  and  one  are  three ;  hence,  she  gave  three 
cents  to  both. 

2.  James  had  two  books,  and  his  father  bought  him  two 
more  ;  how  many  had  he  then  ?  • 


ADDITION. 


3.  In  the  garden  there  are  two  apple-trees,  and  three 
pear-^rees;  how  many  fruit  trees  are  there  ? 

4.  In  a  certain  class  there  are  two  small  girls,  and  four 
large  ones;  how  many  girls  are  in  the  class 2 

5.  I  gave  two  dollars  for  a  pair  of  shoes,  and  "five  dollars 
for  a  silk  hat;  what  did  I  give  for  them  both  ? 

6.  I  pay  two  dollars  a  year  for  a  weekly  paper,  and  six 
df)llars  for  a  daily ;  how  much  do  I  pay  for  both  1 

7.  I  had  two  apples,  and  brother  gave  me  seven  more  ; 
how  many  had  I  then  ? 

8.  If  a  Spelling  Book  cost  two  shillings,  and  an  Arith- 
metic cost  eight  shillings,  what  do  both  together  cost  ?     * 


§  3.     Three  and  one  are  how  many  ? 
+  +  +  -f-  +  +  +  + 

Three  and  two  are  how  many  ? 

+++  ++      +++++ 

Three  and  three  are  how  many  ? 
Three  and  four  are  how  many  ? 
Three  and  five  are  how  many  1    • 
Three  and  six  are  how  many  ? 
'   Three  and  seven  are  how  many  ? 
Three  and  eight  are  how  many  ? 
Three  and  nine  are  how  many  ? 

1.  If  I  walk  three  miles  one  day,  and  two  miles  the  next, 
day,  how  far  do  I  walk  both  days  ? 

Model. — Three  and*two  arc  five;  hence,  I  walk  five 
miles  in  both  dciys. 

2.  If  I  buy  three  pounds  of  butter  from  one  man,  and 
three  pounds  from  an  other,  how  many  pounds  do  I  buy 
from  both  ? 

3.  If  Jane  give  a  beggar  three  cents,  and  John  give  him 
four  cents,  how  much  do  they  botb  give  him  ? 

5 


PRIMARY  ARITHMETIC. 


4.  Mother  gave  three  dollars  for  a  calico  dress,  and  five 
dollars  for  a  muslin  dress ;  what  did  they  "both  cost  her  ? 

5.  John  gathered  three  quarts  of  chestnuts,  and  James 
gathered  six  quarts';  how  many  quarts  had  they  both  ? 

6.  I  earn  three  shillings  a'  day,  and  father  earns  seven 
shillings ;  what  do  we  both  earn  ? 

7.  I  gathered  three  green  apples,  and  eight  r^d  ones; 
how  many  of  both  kinds  did  I  gather  ? 

8.  Johnny  is  three  years  old,  and  his  sister  Sarah  is  nine 
years  older ;  how  old  is  Sarah  ? 


§4.     Four  and  one  are  how  many  ? 

+  -f +  +         +         4- -h  +  +  + 
Four  and  two  are  how  many  ?       • 

+  +  +  +  +-}-      +  +  +  +  +  + 

Four  and  three  are  how  many  ? 
Four  and  four  are  how  many  ? 
Four  and  five  are  how  mar.\  ? 
Four  and  six  are  how  many  X 
Four  and  seven  are  how  many  ? 
Four  and  eight  are  how  many  ? 
Four  and  nine  are  how  many  ? 

1.  A  man  paid  four  dollars" for  some  hay,  and  eight  dol- 
lars for  som»  oats  ;  what  did  he  pay  for  both  ? 

Model.— -Four  and   eight   are  twelve  ;  hence,  he  paid 
twelve  dollars  for  both  ? 

2.  Edward  had  four  marbles,  an-d  Warren  gave  him  three 
more  ;  how  many  had  he  then  ? 

3.  Sallie  gave  four  cents  to  a  beggar,  and  spent  two  cents 
for  candy  ;  how  many  cents  did  she  spend  in  all  ? 

4.  If  a  rocking  chair  cost  four  dollars,  and  a  table  cost 
five  dollars,  what  do  they  both  cost  1 

6 


ADDITION.  §5 


5.  If  I  earn  four  dollars  one  week,  and  six  dollais  the 
next  week,  how  much  do  I  earn  both  weeks  ? 

6.  A  man  gathered  four  bushels  of  apples  from  one  tree, 
atid  seven  bushels  from  an  other ;  how  many  bushels  did 
he  gather  from  both  trees  ? 

7.  Jack  caught  four  squirrels  before  dinner,  and  eight 
after  dinner  ;  .how  many  did  he  catch  all  day  ? 

8.  Lucy  had  four  white  roses,  and  nine  red  ones ;  how 
many  roses  had  she  in  all  ? 


§  5.     Five  and  one  are  how  many  ? 

+  +  +  H--f  +         +-l--h4-  +  + 

Five  and  two  are  how  many  ? 

-f  +  -f  +  +         +H-     +  +  +  +  +  +  + 
Five  and  three  are  how  many  1 
Five  and  four  are  how  many? 
Five  and  five  are  how  many  ? 
Five  and  six  are  how  many  ? 
Five  aind  seven  are  how  many?     « 
Five  and  eight  are  how  many? 
Five  and  nine  are  how  many? 

1.  There  are  five  geese  swimming  on  one   side   of  the' 
pond,  and  one  on  the  other ;  how  many  are  there  in  all  ? 

Model. — Five  and  one  are  six ;    hence,  there   are   six 
geese  in  all.  .  / 

2.  Susan  read  five  pages  of  history,  and  two  pages  oi 
poetry  ;  how  many  pages  of  both  did  she  read  ? 

3.  Emily  had  five  picture  books,  and  Clarence  gave  her 
three. more  ;  hoT7  many  had  she  then? 

4.  In  a  certain. faniily  there  are  five  sons,  and  four  daugh- 
ters ;  how  many  children  are  there  in  the  family  ? 

5..  Thomas  hoed  five  rows 'of  corn  one  day,  and  JoJ:eph 
hoed  five  rows  ;  how  many  rows  did  they  both  hoe  ? 
7 


§6  PRIMARY  ARITHMETIC. 

6.  There  are  five  boys  on  one  bench,  and  sis  on  an  otTier ; 
how  many  are  there  on  both  benches  ? 

7.  I  gathered  five  apples  from  a  tree,  and  left  seven  on 
it*;  how  many  were  there  on  it  at  first? 

8.  "Warren  gave  a  beggar  five  cents,  and  George  gave  him 
eight  cents  ;   how  many  cents  did  they  both  give  him  ] 


§  6.     Six  and  one  are  how  many  ? 

+  +  +  +  +  +         +         +  +  +  +  4-  +  +  ■ 
Six  and  two  are  how  many  ? 

+  +  +  +  +  +         ++      +-F  +  +  -h-f  +  + 
Six  and  three  are  how  many  ? 
Six  and  four  are  how  many  ? 
Six  and  five  are  how  many  7         ^ 
Six  and  six  are  how  many  ? 
Six  and  seven  are  how  many  t 
Six  and  eight  are  how  many  ? 
Six  and  nine  are  how  many  ? 

1.  I  had  six  marbles,  and  my  brother  gave  me  one  more  ; 
how  many  had  I  then  ? 

Model. — Six  and  one  are  seven  ;  hence,  I  had  seven  mar- 
bles then. 

2.  If  I  have  six  books  in  one  hand,  and  two  in  the  other, 
how  many  have  I  altogether  ? 

3.  Charles  gave  six  cents  for  an  orange,  and  three  cents 
Xor  some  nuts  ;  what  did  he  spend  for  both  ? 

4.  Emma  said  six  good  lessons  one  week,   and  four  the 
next ;  how  masy  did  she  say  both  weeks  ? 

5.  Susan's  father  gave  her  six  new  books,  and  her  teacher 
gave  her  five  ;  how  many  did  she  have  then  ? 

6.  Lucy  gave  six  cents  for  a  spool  of  thread,  and  seven 
cent^  for  a  dozen  buttons ;  how  many  cents  did  she  give 

for  both  ? 

8 


ADDITION.  §^7 


7.  William  gathered  six  quarts  of  chincapins,  and  Samuel 
gathered  eight  quarts ;  how  many  quarts  did  both  gather  ? 

8.  If  an  ounce  of  figs  cost  six  cents,  and  a  quart  of  chest- 
nuts cost  nine  cents,  what  will  both  cost  ? 

§  7.     Seven  and  one  are  how  many  ? 

+++++++      +  ++++++++ 

Seven  and  two  are  how  many  ? 

+++++++      ++      +++++++++ 
Seven  and  three  are  how  many  ?     • 
Seven  and  four  are  how  many? 
Seven  and  five  are  how  many  ? 
Seven  and  six  are  how  many  1 
Seven  and  seven  are  how  many  ? 
Seven  and  eight  are  how  many  ? 
Seven  and  nine  are  how  many  ? 

1.  A  farmer  had  seven  cows,  and  bought  two  more ;  how 
many  had  he  then  ? 

Model. — Seven  and  two  are  niae  ;  hence,  he  had  nine 
cows  then, 

2.  Alice  had  seven  cents,  and  her  brother  gave  her  three 
more  ;  how  many  cents  had  she  then  ? 

3.  I  gave  seven  dollars  for  my  coat,  and  four  dollars  for 
my  vest;  what  did  both  garments  cost? 

4.  There  are  seven  sheep  in  one  lot,  and  five  in  an  other  ; 
how  many  are  in  both  lots  ? 

5.  I  gave  seven  dollars  for  a  calf,  and  six  dollars  for  a 
pig ;  what  did  I  give  for  both  animals  ? 

6.  If  a  firkin  of  butter  cost  seven  dollars,  and  a  barrel  of 
vinegar  cost  eight  dollars,  what  do  both  cost? 

7.  A  man  paid  seven  shillings  for  a  night's  lodging,  and 
seven  shillings  for  his  horse's  food  ;  what  did  he  pay  for 
both  ? 

9 


§8  PttlMAaY.  AEJTHMETIC. 


8,  I  paid  seven  dollars  freight  on  a  barrel  of  sugar,  asd 
nine  dollars  on  a  barrel  of  molasses ;  what  did  I  pay  on 
both  ? 


§  8.     Eight  and  one  are  how  macy  ? 

+  +  +  -[-  +  +  +  +    f       +^-4-  +  +  -|-  +  +  + 

Eight  and  two  are  how  many  ? 

+  +  +  +  +  +  +■+      ++      +  +  + ^- +  +  +  +  +  + 

Eight  and  three,  are  how  many? 

Eight  and.four  are  how  many  ? 

Eight  and  five  are  how  many  ? 

Eight  and  six  are  how  many  ?  , 

Eight  and  seven  are  how  many  ?      . 

Eight  and  eight  are  how  many  ?    . 

Eight  and  nine  are  how  many  ?  i   , 

1.  John  owes  one  man  eight  dollars,  and  another  one 
dollar;  what  does  he  owe  them  both  ? 

Model. — l^ight  and  one  are  nine  ;  hence,  he  owes^  theiii 
both  nine  dollars.         '  .  .       '  '"' 

2.  Mary  bought  a  slate  for  eight  cents,  and  a  pencil  for 
two  cents  ;  what  did  she  give  for  them  both  ? 

3.  Jane  has  eight  pins,  and  her  sister  has  three;    how 
many  have  they  both  ? 

4.  Harry  had  eight  cent^^  and  his  brother  gave  him  fonr 
more  ;  how  many  had  he  then?  ,  . ,       . 

5.  James  has  eight  apples,  and  John  has  five;  how  many 
have  they  both  ? 

6.  Pinckney  is  spelled  with  eight  letters,' and  Sallie  with 
six ;  how  many  letters  in  both  their  names  ? 

7.  Charles  bought  eight  oranges,  and  James  bought  sev- 
en'; how  many  have  they  both  1 

8.  Sam  gathered  eight  quarts  of  chestnuts,  and  Joe  gath- 
ered nine ;   how  many  quarts  did  they  IBoth  gather  ? 

10 


ADDITION. 


§  9.     Nine  and  one  are  bow  luanj  ? 

+  +  +  +.+  +  +  +  +      H-         +  +  +  -h  +  +  H-  +  -h  +  * 
Nine  and  two  are  how  many  1 

+  +  +  +  +  +  +  +  +      ++      H-  +  +  -I-  +  +  +  4-  +  +  + 
Nine  and  three  are  bow  many  f 
Nine  and  four  are  liow  many  ? 
Nine  and  five  are  how  many  ? 
Nine  and  six  are  how  many  ? 
Nine  and  seren  are  how  many  ? 
Nine  and  eight  are  how  many  1 
Nine  and  nine  are  how  many  ? 

1.  Mattie  is  nine  years  old  ;  how  old  will  she  he  one  year 

from  this  time  ? 

Model. — Nine  and  one  are  ten ;  hence,  she  will  then  he 
ten  years  old. 

2.  A  farmer  picked  nine  bushels  of  apples  from  one  tree, 
and  three  bushels  from  an  other  ;  how  many  hiishels  did  he 
pick  from  both  ? 

3.  A  man  can  earn  nine  dollars  in  a  week,  and  his  son 
can  earn  four  dollars ;  how  much  can  they  both  earn  ? 

4.  Father  gave  nine  dollars  for  a  set  of  chairs,  and  five 
dollars  for  actable ;  what  did  she  give  for  them  both  1 

5.  Joshua  is  nine  years  old,  and  Joseph  is  six  years  older 
than  he  ;  how  old  is  Joseph  ?  .  ■ 

6.  A  man  gave  nine  dollars  for  a  barl-el  of  flour,  and 
seven  dollars  for  a  keg  of  lard  ;  what  did  he  give  for  both  ? 

7.  James  gathered  nine  quarts  of  walnuts,  and  Alpheus 
gathered  eight  quarts ;  how  many  quarts  had  they  both  ? 

8.  In  a  waiter  there  arc  liine  red- apples,  and  nine  green 
ones;   how  man}"  arc  there  in  all? 

9.  Robert,  bought  a  shot-gun  for  nine  dollars,  and  a  dog 
for  five  dollars;  how  much  did  she  give  for  them  both  ? 

11 


§10  PRIMARY    ARITHMETIC. 


SUBTRACT ION. 

§  10.     One  from  two  leaves  how  maray  1 
(x)x  X 

One  from  three  leaves  how  many  ? 

(x)x  X  XX 

One  from  four  leaves  how  many  ? 
One  from  five  leaves  how  many  ? 
One  from  six  leaves  how  many  ? 
One  from  seven  leaves  how  many  ? 
One  from  eight  leaves  how  many  ? 
One  from  nine  leaves  how  many  ? 
One  from  ten  leaves  how  many  ? 

1.  John  had  two  apples,  and  gave  one  to  his  sister  Mattie  ; 
how  many  had  he  left  1 

Model. — One  from  two  leaves  one  ;  hence,  he  had  one 
apple  left. 

2.  A  beggar  had  three  cents^,  and  lost  one ;  how  many 
cents  had  he  left  ? 

3.  I  had  four  yards  of  cloth,  but  I  cut  off  one  yard  to 
make  a  vest ;  how  many  yards  have  I  remaining  ? 

4.  Joseph  startfcd  to  school  with  five  apples,  but  he  ate 
one  on  the  way  ;  how  many  had  he  when  he  got  there  ? 

5.  Annie  made  six  houses  on  her  slate,  and  then  rubbed 
one  of  them  out ;  how  many  houses  did  she  leave  on  her 
slate  ? 

6.  Jennie  had  s.sven  s^heets  of  paper,  and  gave  Susan  one 
of  them  ;  how  many  sheets  did  she  keep  for  herself? 

7.  Mother  had  ten  chickens,  but  the  cat  killed  one  of 
them  ;  how  many  chickens  has  mother  now  ? 

12 


SUBTRACTION.  §12 


§  11.     Two  from  tliree  leaves  how  many  ?  ^ 

(X  x)  X  X 

Two  from  four  leaves  how  many  ? 

(xx)xx  XX 

Two  from  six  leaves  how  many  ? 
Two  from  seven  leaves  how  many  ? 
Two  h'Om.  eight  leaves  how  many  ? 
Two  from  nine  leaves  how  many  ? 
Two  from  ten  leaves  how  many  1 
Two  from  eleven  leaves  how  many  ?  ,       . 

1.  Agnes  had  five  roses,  and  gave  Ella  two  of  them  ;  how 
many  did  she  keep  for  herself? 

Model. — Two  from  five*  leaves  three ;  hence,  she  kept 
three  roses  for  herself. 

2.  Alice  had  six  dollars,  and  lent  two    dollars   to    Ida  ; 
how  many  dollars  did  she  retain  for  her  own  use  ? 

3.  Mr.  Jones  had  seven  tin  pans,  and  sold  two  of  them ; 
how  many  had  he  left  ? 

4.  There  were  eight  birds  on  a  tree,  and  two  of  them 
flew  away  ;  how  many  were  •left  on  the  tree  ? 

5.  There  were  nine  passengers  in  the  stage,  but  two  of 
them  got  out ;  how  many  remained  in  the  stage  ? 

6.  Johnny  found  ten  eggs,  but  broke  two  before  he  brought 
them  to  his  mother  ;  how  many  did  he  bring  to  her  ? 

7.  "Warren  found  a  tree  with  eleven  apples   on   it,   and 
pulled  them  all  but  two  ;  how  many  did  he  pull  ? 


§  12.     Three  from  four  leaves  how  many  ? 

(x  X  x)x  X 

Three  from  five  leaves  how  many  ? 

(xxx)xx  XX 

Three  from  six  leaves  how  many  ? 

Three  from  seven  leaves  how  many  ? 
13 


^13  PRIMAJLY   ARirnMETIC. 

•  Three  from  eight  leaves  how  many  ? 
Three  from  nine  leaves  how  many  ? 
Three  from  ten  leaves  liow  many  ? 
Three  from  eleven  leaves  how  many  ? 
Three  from  twelve  leaves  how  many  ? 

1.  If  I  make  five  marks  on  my  slate,  and  rub  out  all  but 
three  of  them,  how  many  do  I  rnb  out  ? 

Model. — rThreo  from  five  leaves  two  ;    hence,  I  rub  out 
two  marks. 

2.  I  gave  six  cents  for  a  lead  pencil,  and  sold  it  for  three 
cents ;  how  much  did  I  lose  on  it? 

3.  Father  had  seven  pigs,  but  a  bad  boy  killed  three  of 
them  ;  how  many  has  father  now  1 

4.  Angus  caught  eight  fish,  and  gave  three  of  them    to 
the  miller's  wife  ;  how  many  did  he  keep  for  himself? 

.5.  Carlos  gathered  nine  quarts  of  hazel  nuts,    and    sold 
three,  quarts  of  them  ;  how  many  quarts  did  he  bring  honiQ? 

6.  Carrie  found  a  bush  with  ten  roses  on   it,  and   pulled 
them  all  but  three;  how  many  did  she  pull  1 

7.  Susun  had  twelve  apples.  And  gave  her  sisters  all  but 
three ;  how  many  did  she  give  away  ? 


§  13.     Four  from  five  leaves  how  laauy  ? 

(x  X  X  x)x  X 

Four  from  six  leaves  how  many  ? 

(x  X  X  x)x  X  XX 

Four  from  seven  leaves  how  many  ? 
Four  from  eight  leaves  how  many  f 
Four  from  nine  leaves  how  many  ? 
Four  from  ten  leaves  how  many  1 
Four  from  eleven  leaves  how  many  1 
Four  from  twelve  leaves  now  many  ? 

Four  from  thirteen  leaves  h«w  many  f 
14 


SUBTRACTION.  §14 


1.  Mr,  Jacobs  had  six  acrea  of  larni,  and  gave  four  acres 
to  his  sons  ;  how  many  Acres  did  he  keep  for  himself  ? 

Model. — Four  from  six  leaves  two;  hence,  he  kept  two 
acres  for  himself. 

2.  Mr.  Carpenter  made  seven  gallons  of  vinegar,  aud  sold 
four  gallons ;  how  many  gallons  had  he  left  ? 

3.  Mr.  Kamsour  ground  eight  barrels  of  flour,  and  sold 
all  but  four  barrels  ;  how  many  barrels  did  he  sell  ? 

4.  Mr,  Rhyme  brought  nine  bushels  of  potatoes  to  town, 
but  sold  only  four  bushels ;  how  many  bushels  did  he  take 
home  ? 

6.  Mrs,  SQhrom  made  ten  pounds  of  butter,  and  kept 
only  four  pounds  for  her  own  use  ;  how  many  pounds  did 
she  dispose  of? 

6,  Mr,  Stowe  had  eleven  yards  of  homespun,  and  sold 
four  yards ;  how  much  did  he  retain  for  his  own  use  ? 

7.  Mr,  Plonk  had  eleven  bushels  of  .wheat,  and  sold  all 
but  four  bushels  ;  how  much  did  he  sell  ? 


§  14.     Five  from  six  leaves  how  many  ! 
(xxxxx)x  X 

Five  from  seven  leaves  how  many  ? 

(xxxxx)xx  XX 

Five  from  eight  leaves  how  many  ? 
Five  from  nine  leaves  how  many  ?        ' 
Five  from  ten  leaves  how  many  ? 
Five  from  eleven  leaves  how  many  ? 
Five  from  twelve  leaves  how  many  ? 
Five  from  thirteen  leaves  how  many  ? 
Five  from  fourteen  leaves  how  many  ? 
1.  Mr,  Wingate  had  eight  gallons  of  sorghum  syrup,  and 
sold  five  gallons  ;  how  much  did  he  keep  ? 

15 


§15  PRIMARY   ARITHMETIC. 

Model. — Five  from  eight  leases  three  ;   hence,  he  kept, 
three  gallons. 

2.  Mr.  Collier  had  nine  tons  of  coal,  and  retained  five 
tons  for  his  own  use  ;  how  many  tons  did  he  sell  ? 

3.  Mr.  Miller  had  ten  children,  five  of  whom  were  sons  ; 
how  many  daughters  had  he  ? 

4.  Mr.  Tillett  had  eleven  slaves,  five  of  whom  were  wo- 
men ;  how  many  of  them  were  men  ? 

5.  Mr.  Jenkins  bought  twelve  bushels  of  sweet  potatoes, 
and  sold  five  bushels  ;  how  many  bushels  did  he  keep  ? 

6.  Mrs.  Sumner  went  shopping  with  thirteen  dollars,  and 
brought  five  dollars  home  ;  how  much  did  she  spend  ? 

7.  Mr.  Shuford  hauled  fourteen  loads  of  wood,  and  sold 
five  of  them  ;  how  many  loads  did  he  keep.? 


§  15.     Six  from  seven  leaves  how  many  ? 

(xxxxxx)x  X 

Six  from  eight  leaves  how  many  ? 

(xxxxxx)xx  XX 

Six  from  nine  leaves  how  many? 
Six  from  ten  leaves  how  many  ?  • 

Six  from  eleven  leaves  how  many  1 
Six  from  twelve  leaves  how  many  ? 
Six  from  thirteen  leaves  how  many  ? 
Six  from  fourteen  leaves  how  many  ? 
Six  from  fifteen'  leaves  how  many  ? 

1.  A  tallow-chandler  made  seven  boxes  of  candles   one 
day,  and  sold  six  boxes  ;  how  many  boxes  did  he  keep  1 

Model. — Six  from  seven  leaves  one ;  hence,  he  kept  one 
box. 

2.  A  grocer  bought  nine  casks  of  soda,  and  sold  six  casks  ; 
how  many  casks  had  he  left  ? 

16 


SUBTRACTION.  §16 


3.  A  cutler  made  ten  cases  of  knives  and  forks,  and  sold 
six  cases  ;  how  many  cases  had  he  left  ? 

4.  A  shoemaker  made  eleven  pairs  of  shoes  one  week, 
and  kept  six  pairs  for  his  ownTamily ;  how  many  pairs  did 
he  sell  ? 

5.  A  hatter  had  twelve  wool  hats,  and  sold  six  of  them-; 
how  many  did  he  keep  ? 

6.  A  coachmaker  had  thirteen  buggies,  and  sent  six.  oft' 
th-em  off  to  market ;  how  iftany  did  he  keep  at  home  i 

7.  A  peddler  bought  fifteen  pieces  of  calico  ;  after,  he  had" 
sold  six  pieces,  how  many  had  he  left  ? 


§16.     Seven  from  eight  leaves  how  many.  ? 

(xxxxxxx)x  X 

Seven  from  nine  leaves  how  many  I 

(xxxxxxx)xx  XX 

Seven  from  ten  leaves  how.  many  ? 
Seven  from  eleven  leaves  how  many  1 
Seven  from  twelve  leaves  how  many  ? 
Seven  from  thirteen  leaves  how  many  ? 
Seven  from  fourteen  leaves  how  many  ? 
Seven  from  fifteen  leaves  how  many  ? 
Seven  from  sixteen  leaves  how  many  ? 

1.  John  had  ten  walnuts,  and  gave  his   sister   seven  of 
them  ;  how  many'had'he  left  ? 

Model. — Seven  from  ten  leaves  three  ,  hence,  he  had 
three  waliluts  left. 

2.  James  gathered  eleven  quarts  of  filberts,    and   sold 
seven  quarts  ;  how  many  quarts  did  he  keep  1 

3.  Thomas  caught  twelve  fish,  and  they  were  all  cat-fish 
but  seven  ;  how  many  of  them  were  cat-fish  ? 

4.  Edward  killed  thirteen  robins   and   larks   together ; 
seven  of  them  were  robins  ;  how  many  were  larks  ? 

17  B 


.§17  PRIMARY  AaiTHMETlC. 

5.  Rufus  found  fourteen  eggs,  and  they  were  all  guinea- 
eggs  but  seven  ;  how  many  of  them  were  guinea-eggs  ? 

6.  Lawson  caught  fif teen  j-abb Its  in  his  traps,  but   seven 
of  them  got  away  ;  how  many  did  he  have  then  1 

7.  Joseph  was  sixteen  years  old ;  Benjamin  was  seven 
years  younger  than  he;  how  old  was  Benjamin  ? 


,§17.     Eight  from  nine  leavee  how  many  ? 
(xxxxx,xxx)x  X 

Eight  from  ten  leaves  how  many  ? 
(xxxxxxxx)xx      XX 
Eight  from  eleven  leaves  how  many  ?  ♦ 

Eight  from  twelve  leaves  how  many  ? 
Eiglit  from  thirteen  leaves  how  many? 
Eight  from  fourteen  leaves  how  many  1 
Eight  from  fifteen  leaves  how  many  ? 
Eight  from  sixteen  leaves  how  many  ? 
Sight  from  seventeen  leaves  how  many  ? 

1.  A  man  brought  home  eleven  books,  and  gave  eight  of 
them  to  his  children  ;  how  many  xlid  he  keep  ? 

Model. — Eight  from  eleven  leaves  three ;  hence,  he  kept 
three  books. 

2.  There  were  twelve  girls  in  a  class,  and  eight  of  them 
were  sustained  ;  how  many  were  di^pprDved? 

3.  There  were  thirteen  girls  in  a  class,  and  all  left  school 
but  eight ;  how  many  of  them  left  school  ? 

4.  If  there  are  fourteen  little  girls  in  school,  and  all  but 
eight  have  the  hooping  ccfugh,  how  many  have  it  ? 

5.  If  Susan  brings  fifteen  apples    to  "school,   and   gives 
eigbt  of  them  away,  how  many  htis  she  left  ?^ 

6.  Laura  has  read  sixteen  pages,  all  poetry  but   eight ; 
..how  many  pages  of  poetry  has  she  read  1 

18 


SUBTRACTION.  §18 


'§18.     Nine  from  ten  leaves  liow  many  1 

(xxxxxxxxx)x  X 

Nine  from  eleven  leaves  liow  many? 

(xxxxxxxxx)xx      XX 
Nine  from  twelve  leaves  how  many  ? 
Nine  from  thirteen  leaves  how  many  ?         • 
Nine  from  fourteen  leaves  how  many  ?     « 
Nine  from  fifteen  leaves  liow  many  ? 
Nine  from  sixteen  leaves  how  many  1 
Nine  from  seventeen  leaves  how  many  ? 
Nine  from  eighteen  leaves  how  many 'r' 

i.  Arthur  found  ten  pnrtridge-eggs,  and  brought  home 
nine  of  them  ;  how  maUy  did  he  leave  in  the  nest  ?  • 

Model. — Nine  from  ten  leaves  one;  hence,  he  left  one 
eirff  in  the  nest.    * 

CO 

■  2.  Benjamin  bought  eleven  postage-stamps^  and  used  nine 
of  them  ;  how  many  had  he  left? 

3.  Charles's  father  gave  him  ^twelve  shillings,  and  he 
bought  a  knife  for  nine  shillings  ;  how  many  shillings  had 
he  left? 

4.  David  made  thirteen  tops,  and  kept  nine  of  them  ; 
liow  many  tops  did  he  dispose  of? 

5.  Edward  earned  fourteen  shillings  one  week,  but  spent 
nine  shillings  before  the  end  of  the  we^k ;  how  many  shil- 
lings had  he  Saturday  night  ? 

6.  Frank  gathered  fifteen  quarts  of  chincapins,  and  gave 
^ine  quarts  to  his  little  brothers  and  sisters ;  how  many 

quarts  had  he  left  ? 

7.  George  bought  sixteen  peaches,  and  sold  ther!i  all  but 
nine  ;  how  many  did  he  sell  ? 

8.  Daniel"  had  eighteen  little  lambs,  but  the  dogs  killed 
nine  of  them ;  how  many  had. he  left? 

19 


§l9  PRIMARY   ARITHMETIC. 


MULTIPLICATION. 

g  19.    Twice  one  are  two.  Tvrice  six  are  twelve. 

Twice  two  are  four.  Twice  seven  are  fourteen. 

Twice  three  are  six.  ^        Twice  eight  are  sixteen. 
Twice  fo'ur  are  eight.  Twice  nine  are  eighteen* 

Twice  five  are  ten.  Twice  ten  are  twenty. 

1.  If  one  apple  is  worth  tliree  cents,  what  are  two  apples 
worth  1 

Model. — Twice   three  are  six;    hor<:p^  two  apples  are  , 
worth  six  cents. 

Explanation. — Two  apples  ar»  woiiii  twice  as  much  as 
one  apple,  that  is,  twice  three  cents,  or  six  cents. 

2.  John  bought  two  oranges  at  four  cents  apiece  ;  what 
did  he  give  for  them  both  ? 

3.  Henry*  gave  his  sister  five  cents,  and  Isaac  gave  her 
twice  as  much  ;  how  many  cents  did  Isaac  give  her  ?  « 

4.  If  flour  sells  at  six  dollars  a  barrel,  what  can  I  get  for 
two  barrels  ?  • 

5.  What  is  the  cost  of  two  bilshels  of  wheat,  at  eight 
shillings  a  bushel  ? 

6'.  Seven  days  make  one  week  ;  how  many  days  are  there 
in  two  weeks  ? 

7.  What  cost  two  dozen  Arithmetics,  at  nine  dollars  a 
dozen  1 

§  20.    Three  times  one  are  throe.  Three  times  six  are  eighteen. 

Three  times  two  are  six.  Three  times  seven  are  twenty-one. 

Three  times  three  are  nine.  Three  times  eight  are  twenty-four. 

Three  times  four  are  twelve.  Three  times  nine  are  twenty-seven. 

Three  times  five  are  fifteen.  Three  times  ten  aro  thirty. 

1.  What  cost  three  yards  of  lace,  at  two  cents  a  yard? 

Model. — Three  times  two  are  six  ;  hence,  three  yards 
cost  six  cents. 

20  ■  . 


MULTIPLICATION.  §2! 


2.  What  cost  three  i)ranges,,at  four  cents  apiece  ? 

3.  If  oneft)arrel  of  corn  is  wofth  five  dollars,  what  are 
three  barrels  worth  ? 

4.  If  one  ream  of  paper  is  worth  six  dollars,  what  cost 
three  reams  I 

5.  James  bold  three  quarts  of  chestnuts,  at  seven-  cents  a 
quart ;  how  much  did  he  get  for  them  all  ?     • 

G.  What  cost  three  pounds  of  mutton,  at  eight  cents  a 
pound  y  ^  .     ■ 

7.  A  merchant  sold  three  pairs  of  boots,  at  nine  dollar  a 
pair :  what  did  he  get  for  them  all  ? 


§21.    Four  times  one  are  four.  Four  times  Rix  are  twenty-four. 

Four  times  two  are  eight.  Four  times  seven  are  twenty-eight. 

Four  times  three  are  tvelvo.  Four  times  eight  are  thirty-two. 

Four  times  four  are  sixteen.  Four  times  nine  arc  thirty-six. 

Four  times  five  are  twenty.  Four  times  ten  are  fort3\ 

1.  If  I  walk  three  miles  an  hour,  how  far  will  I  walk  in 
four  hours? 

Model. — Four  times  three  are  twelve;  hence,   I   will 
walk  twelve  miles  in  four  hours. 

2.  If  I  give. four  dollars  apiece  for  four  hats,  what  do  I 
give  for  them  all  ?  ^ 

3.  What  will  cost  four  barrels  of  flour,  at  five  dollars  a 
barrel ? 

4.  How  many  boys  are  there  or^   four   benches,   if  there 
are  six  boys  on  each  bench  ? 

0.  How  much  will  four  yards  of   broajl    cloth    cost,   at 
seven  dollars  a  yard  ? 

6.  What  cost  four  quarts  of  beer,  at  eight  cents  a  quart-? 


§  22.     Five  times  one  are  five.  Five  times  six  are  thirty. 

Five  times  two  are  ten.  Five  times  seven  are  thirty-five. 

Five  times  three  are  fifteen.  Five  times  eight  aie  forty. 

Five  times  four  are  twenty.  Five  times  nine  arc  forty-five. 

Five  times  five  are  twenty-five.  Five  times  ten  are  fifty. 

21 


§23  PRIMARY   ARITHMETIC. 

, • 

1.  A  man  gave  his  five  children'two  shillings  apiece; 
how  much  did  he  give  them  all  ?  ^ 

Model. — Five  times  two  are  ten  ;  hence,  he  gave  them 
all  tea  shillings. 

2.  Mother  has  five  rose-bushes  with  three  roses  on  each  ; 
how  many  roses  are  there  on  them  all  ? 

3.  If  one  bushel  of  wheat  is  vrorth  four  yards  of  domes-' 
tics,  how  many  yards  of  domestics  are  five  bushels  of  wheat 
worth  ?  '^ 

4.  How  much  will  five  head  of  sheep  cost,  at  Q.ve  dollars 
a  head  ?  » 

5.  At  six  shillings  apiece,    iiwit   will  five  Geographies      • 
cost  ? 

6.  At  seven'dollars  a  cord,  what  will  five  cords  of  wood 
cost  ? 

7.  Eight  quarts  make  one  peck ;  how  many  qu.art;s  are 
there  in  five  pecks  ? 

§23.    Six  times  one  are  six.  Six  tiDia^i  ;nx  are  thirty-tiix.    .    . 

Six  times  two  are  twelve.  Six  times  seven  are  forty-two. 

Six  times  three  are  eigbteoa.  Six  times  eight  are  forty-eight. 

Six  times  lour  are  twenty-fonr.  Six  times  nine  are  fiftj'-four. 

Six  times  five  are  thirty.  Six  times  ten  are  sixty. 

1.  If  a  family  eat  one  bushel  of  corn  every  weokj  liov; 
many  bushels  will  last  them  six  weeks  ? 

Model. — Six  times  one  are  six  ;  lience,  six  burdcls  v/ili 
last  them  in  six  weeks.  .  , 

2.  What  will  wx  bushels  of  wheat  cost,  at  tv70  dollars;  a 
bushel  ? 

'  3.  I  bought  six  lead  pencils,  at  three  cents  tipiece;  what ' 
did  I  give  for  them  all  ? 

4.  What  will  six  sheep^cost,  at  six  dollars  a  head  ? 

5.  If  I  get  fo.ur  head-marks  a  day  for  six  days,  bow  many 
will  I  have  then  ? 

22 


MULriPLICATION.  *  §25 


6.  Susan  reads  five  hours  every  day  ;  how   many   hours 
does  she  read  in  six  days  ?  ' 

7.  We  have  six  classes  iu  school,  and  six  girls   in   each 
class  ;  how  many  girls  are  there  in  school  ? 

8.  What  will  six  pounds  of  sugar   cost,  at  tea   cents   a 
pound  ? 


■^  24.    Seron  times  ono  aro  seven.  Seven  times  six  are  forty-two. 

Seven  times  two  are  fourteen.  Seven  times  seven  are  forty-nine. 

Seven  times  three  are  twenty-one  Seven  times  eight  are  fifty-six. 

Seven  times  fonr  are  twenty-eight.  Seven  times  nine  are  sixty-three. 

Seven  times  fivo  aro  thirty-five.  Seven  times  ten  are  seventy. 

1.  Seven  boys  went  chestnut  hunting,  and  gathered  three 
quarts  apiece  ;    how  many  quarts  Iiad  they  all  ? 

Model. — Seven  times  three  are  twenty-one;  hence,  they 
all  had  twenty-one  quarts. 

2.  John  earns  four  dollars  a  week  ;  how  much  does  he 
earn  in  seven  weeks  ? 

8.  At  fire  dollars  a  head,  what  cost  seven  sheep  1 

4.  If  a  daily  paper  cost*six  dollars   a   year,  what    will 
seven  subscriptions  to  it  cost?    - 

5.  There  are  seven  days  in  a  week;  how  many  days  are 
there  in  seven  weeks  ? 

6.  At  eight  dollars  a  day,  what  will  seven  days'  board 
amount  to  ? 

7.  What  will  seven  yards  of  broadcloth  cost,  at  nine  dol- 
lars a  yard  ? 

8.  What  will. seven  yards  of  calico  cost,  at  seven  cents  a 
yard  ? 


§  25.    Eight  times  one  are  eight.  Eight  times  six  are  forty-eight. 

Eight  times  two  are  sixteou.  Eight  times  seven  aro  fifty-.six. 

Eight  times  three  are  twenty-four.  Eight  times  eight  aro  sixty-four. 

Eight  times  four  aro  thirty-two.  Eight  times  nine  are  seventy-two. 

Eight  times  five  aro  forty.  Eight  times  ton  aro  eighty. 

1.  What  will  eight  peaches  cost,  at  two  cents  apiece  ? 
,  2o 


§26  PRIMARY   ARITHMETIC. 

Model. — Eight  times  two  are  sixteen  ;  hence,  they  will 
cost  sixteen  cents.  •  . 

2.  What  will  eight  dozen  "buttons  cost,  at  three  cents  a 
dozen  ? 

3.  What  will  eight  bushels  of  corn  cost,  at  four  shillings 
a  bushel  ? 

4.  Susan  gave  five  cents  apiece  to  eight  beggars;  how 
much  did  she  give  them  all  ? 

5.  How  many  roses  are  there  on  eight  bushes,  if  there 
are  six  roses  on  each  bush  ? 

^,  A  farmer  sold  eight  tons  of  hay  at  seven  dollars  a  ton; 
what  did  he  receive  for  his  hay  ? 

7.  A  lady  sold  eight  pounds  of  butter  at  ten  cents  a 
^ound  ;  what  did  she  get  for  it  all  ? 


g26.    Nine  times  one  are  nine.  Nine  times  six  are  fifty-four. 

Nine  times  two  are  eighteen.  Nine  times  seven  are  sixty-three. 

Nine  times  three  are  twenty-seven.  Nine  times  eight  are  seventy-two. 
Nine  times  four  are  thirty- six.       '      Nine  times  nine  are  eighty-one. 

Nine  tin'ies  five  are  forty-five.  Nine  times  ten  are  ninety. 

1.  Susan  bought  nine  dozen  apples  at  three  cents  a  dozen  ; 
what  did  th^y  cost  her  ? 

Model. — Nine  times  tliree  are  twenty-seven  ;  hence, 
they  cost  her  twenty-seven  cents.  , 

2.  How  many  yards  are  there  in  nine  pieces  of  cloth,  if 
there  are  five  yards  in  each  piece  1 

3.  If  I  travel  six  milesr  an  hour,  how  far  will  I  travel  in 
nine  hours? 

4.  What  will  nine  barrels  of  flour  cost,  at  seven  dollars 
a  barrel? 

•5.  What  will  nine  gallons  of  sorghum  cost,  at  eight  shil- 
lings a  gallon  ? 

6.  If  nine  yards  of  calico  will  make  sister  Mattie  a  dress, 
what  will  a  dress  cost  her,  at  nine  cents  a  yard  ? 

24 


DIVISION.  §27 


DIVISIO'N, 


1 27.     Two  in  two,  onco.  Two  in  twelve,  six  times. 

Two  in  four,  twice.  Two  hi  fourteen,  seven  times. 

Two  in  six,  tliree  times.  Two  in  sixteen,  eight  limes. 

Two  in  eight,  four  times.  Two  in  eighteen,  nine  times. 

Two  in  ten,  five  times.  •  Two  in  twenty,  ten  times. 

When  a  number  is  divided  into  two  equal  parts,  each 
^art  is  called  one  half  of  the  number.  Let  the  above  table 
be  recited  also  as  follows  : — 

One  is  one  half  of  two.  '      Six  is  one  half  of  twelve. 
Two  is  one  half  of  four.  Seven  is  one  half  of  fourteen. 

Three  is  one  half  of  six.  Eight  is  one  half  of  sixteen. 

Four  is  one  half  of  eight.  '    Nine  is  one  half  of  eighteen. 
Five  is  one  half  of  ten.  Ten  is  one  half  of  twenty. 

1.  At  two  cents  apiece,  how  many  peaches  may  be  bought 
for  eight  cents  1 

Model. — The  number  of  peaches  is  equal  to  the  number 
of  times  two  cents  is  contained  in  eight  cents:  two  in  eight, 
four  times  ;  hence,  four  peaches  may  be  bought  for  eight 
cents. 

2.  A  man  divided  fourteen  marbles  equally  between  hie 
two  boys ;    how  many  did  he  give  them  apiece  1 

Model. — He  gave  each  boy  one  half  of  fourteen  marbles: 
seven  is  one  half  of  fourteen  ;  hence,  he  gave  them  seven 
marbles  apiece. 

3.  How  n\any  yards  of  ribbon  at  two  cents  a  yard  can  I 
buy  for  six  cents  ? 

4.  Silas  brought  ten  apples  to  school,  and  gave  them 
equally  to  his  two  class-mates ;  how  many  did  he  give  to 
each  ?       .  , 

6.  At  two  dollars  a  bushel,    how    much    wheat   cap   be 
bought  for  twelve  dollars? 
25 


m 


PR  [  M AEY   ARTTHM  ETi C. 


G„  Last    Christmas,    mother  'divided    qightG'ei 
equali}^  between  si.-^tors  Mary  aiid  Jane;  how  many  oranpes 
em  receive  ?♦ 


did  each  of  th 


Threo  in  eighteen,  six  timos. 
Three  in  twenty-one,  seven  times. 
Three  in  twenty-four,  eight  times. 
Three  in  twenty-seven,  nine  time?. 
Three  in  thirty,  ten  times. 


?  28,    Three  in  three,  once. 
TJirec  in  six,  twice. 
Three  in  nine,  three  times. 
Thro  9  in  twelve,  four  times. 
.Three  in  fifteen,  five  times. 

When  a  number  is  divided  into  three  equal  parts,  each 
part  is  called  one  third  of  tho  number.     Therefore, 

One  is  one  third  of  three.  Six  is  one  third  of  eighteen. 

Two  is  one  third  if  six.  Seven  is  one  third  of  twenty-one. 

Three  is  one  third  of  nine.  Eight  is  one  third  of  twenty-four. 

Four  is  one  third  of  twelve.  Nine  is  one  third  of  twenty-seven. 

Five  is  one  third  of  fifteen.  Ten  is  one  third  of  thirty. 

1.  I  spent  fifteen  dollars  for  corn  at  three  dollars  a  bar- 
rel ,  how  many  barrels  did  I  get  ? 

Model.— The  number  of  barrels  is  equal  to  the  number 
of  times  three  dollars  is  contained  in  fifteen  dollars  :  three 
in  fifteen,  five  tiines  ,  hence,  I  got  five  barrels. 

2.  John,  Andrew,  and  Peter  gathered  eighteen  quarts  of 
chestnuts ;  how  many  quarts  apiece  did  they  gather  ? 

3.  If  a  train  of  cars  run  one  mile  in  three  minutes,  how 
far  will  it  go  in  twenty-one  minutes  ? 

4.  If  three  girls  in  a  class  answer  twenty- four  questions^, 
how  many  does  each  one  answer  ? 

,5.  How  many  pounds  of  butter  at  three  shillings  a  pound 
can  be  bought  for  twenty-seven  shillings  ? 

G.  Joseph  distributed  thirty  cents  among  thrte  poor  chil- 
dren ;  how  many  cents  did  he  give  them  apiece  1? 


[  29.    Four  in  four,  once. 
Four  in  eight,  twice. 
Four  in  twelve,  three  times. 
Four  in  sixteen,  four  times. 
Four  in  twenty,  five  times. 

26 


Four  in  twenty-four,  six  times. 
Four  in  twenty-eight,  seven  times 
Four  in  thirtj^-two,  eight  times. 
Four  in  tlurty-six,  nine  times. 
Four  in  forty,  tea  times. 


division:;  iioO 


When  a  number  is  divided  in  four  equal  parts,  each  part 
is  called  one  fourth  of  tKc  number.     Therefore, 

One  is  one  fourth  of  four.  Six  is  030  fourth  of  twenty-four. 

Two  is  one  fourth  of  eight.  Seven  is  one  foui'th  of  twenty-eight. 

Three  is  one  fourth  of  twelve.  Eight  is  one  fourth  of  tliirty-two. 

Four  is  one  fourth  of  eixteen.  Nino  is  one  fourtli  of  thirty-six. 

Five  is  one  fourth  of  twenty.  Ten  is  one  fourth  of  forty. 

1.  How  many  classes,  of  four  pupils  each,  can  bo  formed 
of  twclva  pupils? 

MoDii^L. — The  iiumbei:  of  classes  i.^  equal  to  the  mimber 
of  times  four  pupils  is  contained  in  twelve  pupils  :  four  in 
twelve,  three  times  ;  hence,  three  classes  can  be  formed. 

2.  A  olasK  of  four  pupils  made  up  twenty  dollars  to  bu)' 
a  present  for  their  teacher;  liow  much  was  that  apiece? 

3.  A  farmer  distributed  eight  bushels  of  potatoes  equally 
among  four  poor  families :  how  many  bushels  did  he  give 
to  each  family  ? 

4.  How  many  primers,  at  four  cents  apiece,  can  you  buy 
for  twenty-four  cents  ? 

5.  HoW' many  books,  at  four  dollars  a  dozen,  may  you 
buy  for  twenty-eight, dollars? 

6.  A  laborer  received  thirty-six  dollars  foi-  four  wcck.^' 
work;  how  much  was  that  each  week? 


§30.    Five  in  five,  once.  Five  in  thirty,  six  times. 

Five  in  ten,  twice.  Five  in  thirty-live,  seven  timcs^ 

Five  in  fifteen,  three  times.  Fiye  in  forty,  eight  tiE\ps. 

Five  in  twenty,  four  tiniea.    '  Five  iu  furty-five,  nine  times. 

Five  in  twenty-five,  five  times.  Five  in  fifty,  ten  times. 

When  a  number  is  divided   into  five  equal  parts,  each 
part  is  called  one  fifih  of  the  number.     Therefore, 

One  ia  one  fifth  offivo.    .  Six  is  one  fifth  of  thirty. 

Two  is  one  fifth  of  ten.  Seven  is  one  fifth  of  thirty-five. 

Three  is  one  fifth  of  fifteen.  Eight  is  one  fifth  of  forty. 

Four  is  one  fifth  of  twenty.  June  is  one  fifth  of  for<-y-five. 

Fire  is  one  fifth  of  twsuty-fivc.  Ten  ia  one  fifth  of  fifty. 

1.  How  many  dozen  eggs,  at  five  cents  a  dozen,  can  you 
buy  for  fifteen  cents  ? 

27 


'§31  PRIMARY/ ARITHMETIC. 


Model. — The  numbe;-  of  dozen  is  equal  to  the  number  of 
times  five  cents  is  contained  in  fifteen  cents :  five  in  fifteen, 
three  times  ;  hence,  three  dozen  eggs  can  be  bought  for  fif- 
teen cents. 

'2.  How  much  broadcloth,  at  five  dollars  a  yard,  may  be 
got  for  twenty  dollars? 

Ji.  How  many  kegs,  each  holding  five  gallons,  will  be  re- 
quired to  hold  twenty-five  gallons  of  vinegar? 

4.  At  what  price  per  barrel  vrould  thirty  dollars  buy  five 
barrels  of  flour  ? 

5.  A  gentleman  divided  thirty-five  picture  books  equally 
among  his  five  Sunday -.school  scholars  ;  how  many  did  each 
one  get? 

6.  I  gave  forty-five  cents  for  five^ spelling  books;  how 
much  did  I  give  apiece  ?  * 


2  31.    Six  in  six,  once.  Six  in  thirty-six,  six  times. 

Six  in  twelve,  twice.  "  Six  in  forty-two,  BeventimeB. 

Six  in  eighteen,  three  times.  Six  in  forty-eight,  eight  times. 
Six  in  twenty-foiir  four  times.  Six  in  fifty-four,  nine  times. 

Six  in  thirty,  five  times,  Six  in  sixty,  ten  times. 

When  a  number  is  divided  into  six  eijual  parts,  each  part 
is 'called  one  sixth  of  the  number.     Therefore, 

One  is  one  sixth  of  six.  Six  is  one  sixth  of  thirty-six. 
Two  is  one  sixth  of  twelve.  Seven  is  one  sixth  of  fortj^-two. 

Three  is  one  sixth  of  eighteen.  Eight  is  one  sixtli  of  forty-eight. 

Four  is  one  sixth  of  twenty-four.  Nine  is  one  sixth  of  fifty-four. 

Five  is  one  sixth  of  thirty.  -  Ten  is  one  sixth  of  sixtj'. 

1.  John  earned  thirt}^  shillings  in  six  days  ;  how  much 
diel  he  earn  each  day  ?  ■       "■ 

Model. — He  earned  each  day  one  sixth  of  thirty  shil- 
lings :  five  is  one  sixth  of  thirty;  hence,  he  earned  five 
shillings  each  day. 

2.  How  long  would  it  take  to  go  twenty-four  miles,  at  six 
miles  an  hour  ? 

?>.  If  stfirch  sells  at  six  cents  a  pound,  how  much  may  be 
bought  for  forty-eight  cents? 

28  « 


DIVISION. 


4.  If  you  read  six  chapters,  of  the  Bible  every  day,  how 
long  would  you  be  in  reading  forty-two  chapters  ? 

5.  A  good  little  girl  memorized  fifty-four  stanzas  in  six 
weeks ;  how  many  stanzas  did  she  memorize  each  week  ? 

G.  Mattie  requires  six  yards  of  gingham  to  make  a  dress* 
she  paid  sixty  cents  for  a  dress  pattern;  what  was  it  a  yard? 


232.    Seven  in  seven,  once.  Seven  in  forty-two,  six  times. 

Seven  in  fonrteen,  twice.  Seven  in  forty-nine,  seven  times. 

Seven  in  twenty-one,  three  times.  Seven  in  fifty-six,  eight  times. 

Seven  in  twenty-eight,  four  times.  Seven  in  sixty-three,  nine  time». 

Seven  in  thiHy-five,  five  times.  Seven  in  seventy,  ten  times. 

When  a  number  is  divided  into  seven  eq^ual  parts,  each 
part  is  called  one  seventh  of  the  number.     Therefore, 

One  is  one  seventh  of  seven.  Six  is  one  seventh  of  forty-two. 

Two  is  one  seventh  of  fourteen.  Seven  is  one  seventli  of  forty-nine. 

Throe  is  one  sovcnth  of  twenty-one.  Eight  is  one  seventh  of  fifty-six. 

Fonr  is  one  seventh  of  twenty-eight.  Nine  is  one  seventh  of  sixty-three. 

Five  is  one  seventh  of  thirty-five.  Ten  is  one  seventh  of  seventy. 

1.  If  seven  boys  sit  on  a  bench,  how  many  benches  will 
be  required  for  twenty-one  boys? 

Model. — The  number  of  benches  is  equal  to  the  number 
of  times  seven  boys  is  contained  in  twenty-one  boys:  seven 
in  twenty-one,  three  times;  hence,  three  benches  will  be 
req'uired  for  twenty-one  boys. 

2.  If  seven  yards  of  ribbon  cost  forty-nine  cents,  what 
does  one  yard  cost  ? 

3.  Mr.  Goodman  gave  thirty-five  marbles  to  his  seven 
children ;  how  many  did  he  give  them  apiece? 

4.  A  stage-coach  runs  forty-two  miles  in  seven  hours ; 
how  many  miles  an  hour  does  it  run  1 

5.  In  a  school  of  fifty-six  pupils,  there  are  seven  pifpih 
in  each  class ;  how  many  classes  are  there  ? 

6.  I  gave  seventy  cents  for  seven  yards  of  domestics ; 
what  was  that  a  yard  ?  ^  ^ 

29 


j33     '  primIry*  arithmetic. 


g  33.    Eight  in  eight,  once.  Eight  in  forty-eight,  six  times. 

Eight  in  sixteen,  twice.  Eight  in  fifty-six,  seven  times. 

Eight  in  twenty-four,  three  times.  Eight  in  sixty-four,  eight  times. 

Eight  in  thirty-two,  four  times.  Eight  m  seventy-two,  nine  timee. 

Eight  in  forty,  five  times.  Eight  in  eighty,  ten  times. 

When  a  DTiiiiber  is  divided  into  eight  equal  parts,  each 
part  is  called  one  eighth  of  the  number.     Therefore, 

One  is  one  eighth  of  eight.  Six  is  one  eighth  of  forty-eight. 

Two  is  one  eighth  of  sixteen.  Seven  is  one  eighth  of  fifty-six. 

Three  is  one  eighth  of  twenty-four.  Eight  is  one  eighth  of  sixty-four. 

Four  is  one  eighth  of  thirty-two.  Nine  is  one  eighth  of  seventy-two. 

Five  is  one.  eiglith  of  forty.  Ten  is  one  eighth  of  eighty. 

1.  If  eight  head  of  sheep  cost  twenty-four  dollars,  what 
does  one  sheep  cost? 

Model. — One  sheep  costs  one  eighth  of  twenty  four  dol- 
lars: three  is  one  eighth  of  twenty- four;  hence,  one  sheep 
costs  three  dollars. 

.  '2.  If  eight  work  hands  eat  sixteen  pounds  of  meat  in  a 
day,  how  much  does  one  hand  eat  ? 

§34.    Nine  in  nine,  once.  Nine  in  fifty-four,  six  times. 

Nine  in  eighteen,  twice.  Nine  in  sixty-three,  seven  times. 

Nine  in  twenty-seven,  three  times.  Nine  in  seventj'^-two,  eight  times. 

Nine  in  thirty-six,  four  times.  Nine  in  eighty-one,  nine  times. 

Nine  in  forty-five,  five  times.  Nine  in  ninety,  ten  times. 

When  a  number  is  divided  into  nine  equal  parts,  each 
part  is  called  one  nintli  of  the  number.     Therefore, 

One  is  one  nJnth  of  nine.  Six  is  one  ninth  of  fiftj'^-four.  , 

Two  is  one  ninth  of  eighteen.  Seven  is  one  ninth  of  sixty-three. 

Three  is  one  ninth  of  twenty-seven.  Eight  is  one  ninth  of  seventy-two. 

Four  is  one  ninth  of  thirty-six.  Nine  is  one  ninth  of  eighty-one. 

Five  is  one  ninth  of  forty-five.  Ten  is''  one  ninth  of  ninety. 

1.  At  nine  dollars  a  yard,  how  much  cloth  will  cost  tvcen- 
ty-seven  dollars? 

Model. — The  number  of  yards  is  equal  to  the  number  of 
times  nine  dollars  is  contained  in  twenty-fEeven  dollars : 
nine  in  twenty-seven,  three  times ;  hence,  three  yards  will 
cost  twenty-seven  dollars. 

2.  If  I  divide  forty-five  apples  equally  among  nine  girls, 
how  many  apples  will  each  girl  receive  ? 

30 


BART    U. 

.  — — .*»»- 

NOTATION     AND^  ADDITION. 
§  35.     Numbers  are  represented  by  figures. 


The  number 

one  is 

represented  by 

the 

figure 

1 

«          (( 

two 

u 

o 

«            u 

three 

« 

ti 

3 

((            <. 

four 

" 

a 

4 

<(            « 

five 

(( 

<;• 

5. 

«            ;< 

SIX 

t      f( 

u 

■  6 

«            c> 

seven 

« 

(1 

7 

<;            « 

eight 

« 

« 

8 

<c           « 

■niTift 

<; 

Ci 

0 

These  nine  figures,  together  with  one  other,  0,  naught, 
may  be  combined  so  as  to  represent  all  the  numbers  in 
existence.  The  methods  of  combining  them  will  be  ex- 
plained as  we  progress. 

1.  Father  paid  2  dollars  for  a  cord  of  wood,  3  dollars  for 
a  load  of  hay,  and  8  dollars  for  a  pig  ;  what  did  he  give  for 
them  all  ?  . 

Model. — 2  and  3  are  5,  and  8  are  thirteen  ;  hence,  he 
gave  thirteen  dollars  for  them  all. 

3.  Mr.  Joiner  sold  a  set  of  chairs  for  5  dollars,  a  work- 
stand  for  7  dollars,  and  a  center-table  for  9  dollars ;  what 
did  he  get  for  them  all  ? 

3.  Mr.  Carpenter  made  me  a  set  of  sash  for   4   dollars, 
furnished  the  glass  for  5  dollars,  and  charged  3  dollars  for 
putting  them  in  ;  what  was  the  whole  of  his  bill  'i 
31 


§36  PRIMARY   ARITHMETIC. 


4.  A  provision  train  went  6  miles  oiie  day,  7  miles  the 
next  day,  and  8  miles  the  next  day ;  how  far  did  it  go  in 
the  three  days  ? 

5.  Lucy  gave  5  cents  for  a  spool  of  thread,  8  cents  for  a 
paper  of  needles,  and  9  cents  for  a  thimble  ;  what  did  she 
give  for  them  all  ? 

6.  A  shepherd  has  8  sheep  in  one  lot,  9  sheep  in  an  other, 
and  7  sheep  in  a  third ;  how  many  has  he  in  all  ?' 


236.      Tea  id 

denoted 

10. 

Fifteen  is 

denoted 

15. 

Eleven 

K 

11. 

Sixteen 

a 

16. 

Twelve 

u 

12. 

Seventeen 

a 

17. 

Thirteen 

a 

.13. 

Eighteen 

ii 

18. 

Fourteen 

a 

14. 

Nineteen 

<( 

19. 

1.  There  are  12  girls  in  the  first  class,  9  girls  in  the  sec- 
ond, jind  8  girls  in  the  third ;  how  many  girls  arfe  in  those 
three  classes  ? 

2.  John  brought  his  mother  14  walnuts,  Willie  brought 
her  8,  and  Lee  brought  her  6 ;  how  many  walnuts  did  they 
all  bring  ]      . 

3.  A  drover  bought  15  cows  from  ons  man,  5  from  an 
other,  and  7  from  an  other ;  how  many  did  he  buy  from 
them  all?  • 

4.  Thomas  had  3  quarts  of  hazel  nuts,  Robert  gave  him 
6  quarts  more,  and  Joseph  gave  him  9  quarts  more  ;  how 
many  had  he  then  ? 

5.  A  laborer  earned  8  dollars  one  week,  7  dollars  the 
next,  and  9  dollars  the  ne»t ;  how  much  did  he  earn  in  all? 

6.  Sue  wrote  7  lines  one  day,  Sallie  wrote  6  lines,  and 
Mary  wrote  8  lines;  how  many  lines  did  they  all  write  ? 


§37.      Twenty  is 

denoted 

20. 

Twenty-five  is 

denoted 

25. 

Twenty-one 

a 

21. 

Twenty-six 

ii 

26. 

Twenty-two 

<( 

22. 

Twenty-seven 

11 

27. 

Twenty-three 

• 

23. 

Twenty-eight 

i( 

28. 

Twenty-four 

24.     - 

Twentyrnine 

<; 

29. 

32 

NOTATION    4.ND   ADDITION.  §38 

1.  John  bought  a  knife  for  27  cents,  a  top  for  8  cents, 
and  a  whip  for  10  cents ;  what  did  he  give  for  them  all  ? 

2.  A  workman  sold  a  hand-cart  for  28  dollars,  and  a 
wheelbarrow  for  8  dollars  ;  what  did  he  receive  for  them 
both? 

3.  A  small  farmer  raised  27  bushels  of  wheat  on  one  lot, 
and  9  bushels  on  an  other ;  what  did  he  raise  on  both  ? 

4.  A  man  bought  24  dollars*  worth  of  wheat,  9  dollars' 
worth  of  corn,  and  8  dollars'  worth  of  pork;  what  did  he 
pay  for  all  ? 

5.  A  lady  gave  27  dollars  for  a  silk  dress,  8  dollars  for 
trimming,  and  5  dollars  for  making  it;  what  did  her  dr6ss, 
cost  her  ? 

G.  Charles  gave  22  cents  for  a  Primary  Arithmetic,.  lO'? 
cents  for  a  Spelling  Book,  a»d  8  cents  for  a  copy-book  i^ 
what  did  the  three  cost  him? 


gSS.      Thirty  is 

denoted 

30. 

Thirty-five  is 

denoted- 

35, 

*  Thirty-one 

li 

31. 

Thirty-six 

'<,. 

36. 

Thirty-two 

e( 

32. 

Thirty  scvea, 

a . 

37. 

Thirty-three 

a 

33. 

Thirty-eight 

'i 

38. 

Thirty-four 

a 

U. 

Thirty- nin  3 

a 

39. 

^ 


1.  There  are  31  sheep  in  one  pasture,.and  10  in  the  other; 
how  many  are  there  in  both  ? 

2.  A  bookseller  sold  36  Arithmetics)  9  Grammar^;  and  8 
Headers;  how  many  books  did  be  sell  in  all  ? 

3.  A  housekeeper  spent  35  dollars  for  flour,  8  dollars  for 
meal,  and  7  dollars  for  vegetables ;.  what  did  they  •  all 
amount  to  ? 

4.  Deuteronomy  has  34  chapters,    Ezra  10  chapters,  and 
Lamentations  5  chapters;  how  many  chapters  are  there  in, 
these  three  books  1  '  '    - 

5.  Mr.  Jones  is  37  years  old,  his  son  John  is  9  years  old, 
and  his  daughter  Ella  6  ;  what  do  their  ages  all  amount  to  ?. 

33  C 


§39 


PRIMARY   AlUTpMETTO. 


6.  Sallie  called  to  visit  her  country  .cousin,  and  spent  the 
last  10  days  of  June,  the  whole  of  July,  and  the  first  6  days 
of  August ;  how  long  was  her  visit  ? 


§39.       Forty  is  denoted 

40. 

Fifty  is   denoted 

50. 

Forty-ono            . " 

41. 

Fifty-one 

61. 

Forty-two              " 

■12. 

Fifty-two 

li 

52. 

Forty-three           " 

43. 

Fifty-three 

'• 

53. 

^oj-ty-four             •' 

44. 

Fifty-four 

i( 

54.. 

:Forty-five              " 

45. 

Fifty-five 

•i 

55. 

■  Forty-six               "* 

46. 

Fifty-six 

ti 

56. 

..Forty-s3veu          "  - 

47. 

Fifty-seven 

u 

57. 

Forty-eight           " 

48. 

Fifty-eight. 

ii 

58. 

Forty-nine             " 

49. 

Fifty-ninb 

(1 

59. 

'1.  A  merchant  collected  45  dollars  from  one  customer, 
tand  9  dollars  froisa  an  other  ;  how  much  did  he  collect  from 
both?  -'  * 

2.  Mr.  Tiller  gave  48  dollars  for  a  carry-all,  and  8  dol- 
lars for  a  set  of  harness.;  what  did  he  give  for  them  both? 

3.  A  grocer  sold  one  customer  50  pounds  of  sugar,  an 
other  10  pounds,  and  a  tbird  6  pounds ;  how  many  pounds 
did  he  sell  to  the  tbreCf? 

4.  A  merchant  had  four  customers  one  day;  from  one  he 
received  55  dollars,  from  an  other  3  dollars,  from  an  other 
7  dollars,  and  from  the  other  8  dollars ;  what  did  he  re- 
ceive that  day  ? 

5.  Mattie's  dress  cost  56  cents,  the  trimming  cost  9  cents, 
and  the  thread  and  buttons  8  cents;  what  did  it  all  cost? 

6.  Bought  butter  for  54  cents,  eggs  for  10  cents,  and 
fruit'for  8  cents  ;  what  did  they  all  cost? 

J.  A  bookseller  sold  to  a  teacher  48  Grammars,  7  Arith- 
metics, and  9  Spelling  Books;  how  many  books  did  he  «ell? 

,8.  A  farmer  sold  a  horse  for  55  dollars,  and  a  cow  for  9 
dollars ;  what  did  he  get  for  both  ? 

9.  An  orchard  contains  58  apple  trees,  8  pear  trees,  and 
7  cherry  trees ;  how  many  trees  are  in  the  orchard  ? 


NOTATION   AND   ADDITION. 


§41 


^40.      Sixty  is 

denoted 

CO. 

Seventy    is    denoted 

70. 

Sixty-one 

(i 

ei. 

Seventy-one       " 

71. 

Sixty-two 

•' 

62. 

Seventy-two      " 

72. 

Sixty-three 

" 

63. 

Seventy-three  " 

73. 

Sixty-four 

u 

64. 

Seventy-four     ^ 

74. 

Sixty  five 

" 

65. 

Seventy-five      " 

75. 

Sixty-six 

t( 

60. 

Seventy-six       " 

76, 

Sixty-Bevea 

u 

67. 

Seventy-seven  " 

77.    . 

Sixty-eight 

". 

68. 

Seventy-eight   " 

78. 

Sixtj'  nine 

u 

69. 

Seventy-nine     " 

79. 

1.  Joseph  gave  60  cents  for  a  pen-knife,  and  15  cents  for 
a  whip  ;  what  did  he  give  for  them  both  ? 

2.  Josephine  bought  a  handkcrchief.for  70  cents,  some 
hooks  and  eyes  for  17' cents,  and  some  lace  for  9  cents; 
what  did  she  give  for  them  all  ? 

3.  Laura  bought  a  gross  of  steel  pens  for  75  cents,  a  quire 
uf  paper  for  18  cents,  and  a  pack  of  envelopes  for  10 cents ; 
what  did  she  give  for  them  all  ? 

4.  Mr.  Hauser  gave  77  dollars  for  a  barrel  for  sugar,  and 
had  to  pay  3  dollars  for  the  barrel,  and  15  dollars  freight 
on  it ;  what  did  the  whole  cost  him  ? 

5.  Mr.  Plowman  gave  78  dollars  for  a  yoke  of  oxen,  and 
25  dollars  for  a  cart  and  fixtures  ;  what  did  he  give  for 
both? 


41.      EigHty    is 

• 
denoted 

80. 

Ninety    is     denoted 

90. 

Eighty-one 

iC 

81. 

Ninety-one 

-' 

91. 

Eighty-two 

(( 

82. 

Ninety-two 

a 

92. 

Eighty-three 

u 

83. 

Ninety-three 

«         • 

93. 

Eighty-four 

u 

84. 

Ninety-four 

94. 

Eighty-five 

u 

85. 

Ninety-five 

95. 

Eighty-six 

.( 

86. 

Ninety-six 

96. 

Eighty-seven 

(( 

87. 

Ninety-seven 

"• 

97. 

Eighty-eight 

'• 

88. 

Ninety-eight 

98. 

Eighty-nine 

ii 

89. 

Ninety-nine 

99. 

1.  I  sold  some  pork  for  88  dollars,  and  some  potatoes  for 
15  dollars  ;  what  did  I  get  for  them  both  ? 

2.  f»  bought  a  horse  for  90  dollars,  and  a  cow  for  17  dol- 
lars ;  what  did  the  two  cost  me  ? 

35 


S42 


PRIMARY   ARITHMETIC. 


3.  I  laid  out  85  dollars  for  sugar,  and  13  dollars  for  tea  ; 
how  much  did  I  lay  out  ? 

4.  Mrs.  Puny  weighs  89  pounds,  and  her  child  weighs 
10  pounds ;  what  is  their  united  weight  ? 

5.  A  farmer  sold  81  sheep  and  had  only  18  left  ;  how 
many  had  he  at  first  ? 

6.  Mr.  Truly  sold  80  bushels  of  wheat,  gave  8  bushels  to 
soldiers'  wives,  and  laid  aside  12  bushels  for  seed  ;  how 
much  of  his  crop  did  he  dispose  of  in  these  ways? 


NOTATION    AND     S  UB  TK  A  C  T  10  N  .. 


2  42.    One  hundred 
One  hundred  and  one 
One  hundred  and  two 
•  One  hundred  and  three 
One  hundred  and  four 
One  hundred  and  five 
One  hundred  and  six 
One  hundred  and  ten 
One  hundred  and  eleren 
One  hundred  and  seventeen 
One  hundred  and  twenty 
One  hundred  and  thirty-one 
One  hundred  and  forty-four 
Ohe  hundred  and  fifty-eight 
Cue  hundred  and  seventy-two 
One  hundred  and  eighty-five 
One  hundred  and  ninety-nine 

Write  one  hundred  and  five,  one  hundred  and  sixteen, 
one  hundred  and  thirty-five,  one  hundred  and  for.ty-nine, 
one  hundred  and  seventy-five. 

Read  112,  107,  125,  179,  188,  193. 

1.  A  man  went  to  town  with  113  dollars,  and  spenj  all 
he  had  but  9  dollars  ;  how  much  money  did  he  spend  ? 
36 


is  denoted 

100. 

a 

101. 

a 

102. 

.  a 

103. 

a 

104. 

(i 

105. 

(( 

lOG. 

a 

110. 

a 

111. 

u 

117. 

a 

120. 

(( 

"ISI. 

a 

144. 

« 

15S. 

<> 

172. 

ii 

185. 

ii 

199. 

NOTATION    AND   SUBTRACTION.  §48 

Model. — 9  from  113  leaves  104  ;  hence,  he  spent  104 
dollars. 

2.  A  farmer  raised  127  bushels  of  wheat,  and  reserved 
11  bushels  for  seed  ;  how  much  had  he  besides  ? 

8.  A  man  bought  a  buggy  for  135  dollars,  and  sold  it  at 
a  loss  of  13  dollars  ;  how  much  did  he  get  for  it  ^ 

4.  Miss  Sallie  Brown  went  off  to  a  boarding  school  with 
145  dollars,  and  had  only  8  dollars  left  at  the  end  of  the 
session  ;  v/Lat  were  the  session's  expenses? 

5.  Little  Johnny's  book  has  166  pages,  and  he  has  read 
all  but  9  pages  ;  how  many  pages  has  he  read  't 

6.  Mr.  Planter  raised  180  bushels  of  ground  peas,  and 
kept  15  bushels  for  his  own  use  ;  how  many  bushels  did  he 
dispose  of  ? 


g  43.    Tw»  hundred  is  denoted        200. 

Two  hundred  and  one  "  201. 

Two  hundred  and  five  '•  205. 

Two  hundred  and  ten  ''  210. 

Two  hundred  and  fifteen                    »  '•  215. 

Two  hundred  and  twenty-five  "  225. 

Two  luindred  and  thirty-seven  ''  237. 

Two  hundred  and  forty-nine         •  "  249. 

Two  hundred  and  sixty-six  "  2CG. 

Two  hundred  and  seventy-five  ••  275. 

Two  hundred  and  eighty  '•  280. 

Two  hundred  and  ninetj'-eight  "  298. 

Write  two  hundred  and  three,  two  hundred  and  eleven, 
two  hundred  and  twenty-two,  two  hundred  and  thirty,»two 
hundred  and  fifty-five,  two  hundred  and  seventy-seven. 

Read  207,  214,  228,  235,  244,  258,  297. 

1.  Mr.  Smith  sold  a  horse  for  225  dollars,  and  gained  10 
dollars  by  the  bargain ;  what  did  the  horse  cost  him  ? 

2.  Mr.  Coulter  raised  200  bushels  of  corn,  and  paid  9 
bushels  tax  ;  how  mucb  had  he  left  ? 

37 


§44  PRIMARY   ARITHMETIC. 


3.  Mr.  Finger  made  215  gallons  of  sorghum,  and  lost  II 
gallons  by  leakage ;  how  many  gallons  had  he  left  f 

4.  Mr.  Carpenter  raised  100  bushels  of  wheat  on  one 
field,  and  125  bushels  on  an  other ;  he  paid  20  bushels  for 
having  it  threshed  ;   how  much  had  he  remaining? 


§■44,    I'hree  hundred 

is  denoted 

300. 

Three  hundred  and  three 

"  . 

303. 

Three  hundred  and  fifteen 

a 

315. 

Three'hundred  and  twenty-one 

" 

821, 

Tkree  hundred  and  thirty-three 

" 

333. 

Three  hundred  and  fifty-six 

'« 

356. 

Three  hundred  and  eighty  niiic 

'■ 

359, 

Write  three  hundred  and  one,  three  hundred  and  ten, 
three  hundred  and  seventeen,  three  hundred  and  thirty, 
three  hundred  and  forty-three,  three  hundred  and  sixty ^six. 

Read  308,  313,  327,  349,  352,  390,  399. 

1.  I  had  325  dollars,  but  I  had  to  pay  12  dollars  tax  on 
it ;  how  much  money  Had  I  left  ? 

2.  A  traveler,  whose  journey  wa.s  350  miles,  has  finished 
it  all  but  20  miles ;  ^how  far  has  he  gone  ? 

3.  Susan  hnp  rend  a.i  but  15  pages  of  a  book  of  368 
pages  ;  how  many  pages  has  she  read  ? 

4.  A  grocer  bought  a  barrel  of  sugar  weighing  376 
pounds  gross;  the  barrel  weighed  14  pounds;  how  many 
pounds  of  sugar  did  he  buy  ? 


2  45.    Four  linudred 
Four  hundred  and  four 
Four  hundred  and  seven 
Four^hundred^and  fourteen     " 
Four  hundred  and  forty. 
Four  hundred  and  forty  four 
Four  hundred  and  fifty-four 

Write  four  hundred  and   seventeen,  four  hundred   and 


ts  deuottd 

400. 

404. 

407. 

414. 

440. 

444. 

454. 

NOTAriON'    AND    SUBTHACriON. 


§4G 


twenty- eight,  four  liundi-ed  and  thirty-nine,  four  hundred 
and  eighty,  four  hundred  and  ninety-six. 

Read  418,  422,  430,  449,  450,  478,  487. 

1.  A  farmer  raised  420  bushels  of  corn,  and  sent  25 
bushels  to  his  pastor  ;    how  many  budiels  ha4  he  left  ? 

2.  ^  man  took  450  dollars  to  town,  hut  spent  only  16 
dollars;    how  much  did  he  bring  home  ? 

o.  A  butcher  killed  a  beef  weighing  418  poundp,  and 
kept  16  pounds  for  his  own  use  ;    how  much  did  he  gell  ? 

4.  A  trader  sold  a  pair  of  horses  for  435  dollars,  and 
gained  15  dollars  by  the  trade  ;  what   did   the  horses    cost 


hi 


m 


% 
2  46.     Fivo  hundred 

is  denoted 

500. 

Five  hundred  and  fivo 

<c 

505. 

Five  hundred  and  fifteen 

a 

515. 

Five  hundred  and  fifty 

" 

550. 

Five  hundred  and  fifty-five 

•• 

555. 

Five  hundred  and  forty-nine 

u 

549. 

Fivo  hundred  and  eighty-seven 

587. 

Write  five  hundred  and  eighteen,  five  hundred  and  six 
five  hundred  and  twenty-seven,  five  hundred  and  forty-nine 
five  hundred  and  sixty-eight,  five  hundred  and  nipety-four- 

Read  507,  509,  575.  524,  536,  547,  563,  585. 

1.  A  man,  who  had  504  acres  of  land,  sold  24  acres  ;  how 
much  had  he  remaining  ? 

2.  A  farmer  raised  100  bushels  of  corn  at  one  plantation, 
and  427  bushels  at  an  other  ;  he  sent  26  bushels  to  mill ; 
how  much  had  he  left  ? 

3.  My  Philosophy  has  536  pages,  and  I  lack  on]>y  32 
pages  of  being  through  it ;  how  many  pages  have  I  studied  ? 

4.  I  sold  a  carriage  f'or  550  dollars,  and  thereby  gained 
47  dollars ;    what  did  it  cost  me  I 

39 


U7  PRIMARY   ARITHMETIC. 


2 -47.    Six  hundred 

-, 

is  denoted 

600. 

Six  hundred  and  six 

<( 

606. 

Six  hundred  and  sixteen 

(. 

616. 

Six  hundred  and  ninety-nine 

ii 

699. 

Seven  hundred 

" 

700. 

Seven  hundred  and  seven 

<.' 

707. 

Seven  hundred  and  soventj'-eeven 

(( 

777. 

Seven  hundred  and  eighty-four 

It 

784. 

Write  six  hundred  and  tliirty-fourj  six  hundred  and  for- 
ty-,three,  six  hundred  and  fifty-seven,  six  hundred  and  sev- 
enty-five, seven  hundred  and  fifty-six,  seven  hundred  and 
sixty-five,  seven  hundred  and  ninety-nine. 

Read  626,  662,  638,  683,  741,  714,  729,  792. 

1.  I  am  reading  a  Historyjn  two  volumes;  the  first  vol- 
ume has  400  pages,  and  the  second  has  350  ;  I  am  within 
45  pages  of  being  through  the  second  -^olume;  hcnv  many 
pages  have  I  read  ? 

2.  Brother  John  is  reading  the  same  History,  and  has  30 
pages  of  the  first  volume  yet  to  r^ad  ;  how  many  pages  has 
he  to  read  in  all  ? 

3.  James  gathered  425  chincapins  yesterday,  and  gaT« 
away  25  ;  to-day  he  has  gathered  300  more;  how  many  has 
he  now  ? 

4.  Mr.  Sykes  sold  47  acres  from  a  tract  of  650  acres  ^  how 
much  land  had  he  remaining  ? 


148.    Eight  hundred 
Eight  hundi  ed  and  one 
Eight  hundred  and  eight 
Eight  hundred  and  eighteen 
Nine  hundred 
Nine  hundred  and  nineteen 
Nine  hundred  and  ninety 
Nine  hundred  and  ninety-nine 


is  denoted 

800. 

li 

801. 

« 

808. 

a 

818. 

a 

900. 

(( 

919. 

(( 

990. 

t< 

999. 

Write  eight  hundred  and  fifteen,  eight  hundred  and  fifty- 
one,  eight  hundred  and  forty-seven,  eight  hundred  and  tev- 

40 


NOrATJON    AND    MULTiriUCATlON. 


§49 


ent}'*four.,  nine  hundred  and  fiixtj-thr^e,  nine  hundred  and 
seventy-nine,  nine  hundred  and  ninety-seven. 
Read  823,  S82,  849,  894.  948,  984,  <)57,  975. 

1.  There     arc    929    chapters    in    the    Old    TcL-tament; 
Zechariah  has  14  chapters,  and  Malachi  4;  bitter  Susan  has 
read  all  bub  thci^e  two  books;  how  many  chapters  has  she,, 
read  ? 

2.  There  are  150  Psalms  in  the  Bible;  how  many  cha'p- 
ters  are  there  lu  the  Old  Testament  besides  the  Pi^alnisi' 

3.  The  New  Testament  has  260  chapters-;  the  Revelation 
bas  22 ;  how  many  chapters  are  in  all  the  other  boohs  t 

4.  Mattie  has  ro«id  the  book  of  Matthew,  which  has  28 
chapters ;  how  many  more  chapters  has  she  to  read  ? 


-«♦»- 


NOTATI0.N     AND     MULTIPLICATION. 


is  dev 


oted 


1000. 
1001. 
1011. 
1101. 
1110. 
1211. 
1717. 
1999. 


4  49.    Cue  thousand 
One  thousand  and  ono 
One  thousand  and  el*vcn  * 

One  thousand  one  hundred  and  one 
One  thousand  one  hundred  and  ten 
One  thousand  two  hundred  and  eleven 
One  thousand  seven  hundred  and  seventeen 
,  On*  thousand  nine  hundred  and  ninety-nine 

"Write  one  thousand  one  hundred  and  forty,  one  thousand 
two  hundred  and  twenty-five,  one  thousand  four,  hundred 
and  sevQuty-nine,  one  thousand  and  ninety  seven,  one  thou- 
sand six  hundred  and  sixty-one,  one  thousand  one  hundred 
and  sixty-six,  one  thousand  six  hundred  and  sixteen. 
.    Read  1007,  1207,  1220,  1203,  1033,  1330,  1429,  1492. 

'1.  What  cost  7  yards  of  lace,  at  3  cents  a  yard  ? 

n 


§50  PHI.MARY    -VRITHrvIETIG 


Model. — 7  times  3  arc  21  ;  heocGj  7  yards  cost  21^8uts, 
Explanation. — 7  yards  cost  7  tiaies  as  mucli   as  one 

yard,  that  is,  7  times  3  cents,  or  21  cents. 

;^n'fl.. — r>o  carofal  not  tn  alifi'.r  f.he  pupil  to  say  3  ti'iic-  7,  for  7 

tirrjes  o 

2.  What  cost  3  quarts  of  chestnuts,  at  8  cents  a  quart  ? 

3.  If  1  yard  of  dloth  cost  5  dollars,  what   will  5  yards 
eost? 

4.  I  bought  4  barrels  of  flour,  at  7  dollars  a  barrel ;  what 
did  T  pay  for  the  four  ? 


is  denoted 

2000. 

li 

2001. 

u 

2002. 

ii. 

2020. 

ii 

2022. 

i. 

9220. 

li 

2325. 

li 

2436. 

^50.    Two  thousand 
Two  thousand  and  one 
Two  thousand  and  two 
Two  thousand  and  twenty 
Two  thousand  and  twenty-two 
Two  thousand  two  hundred  and  twenty 
Two  thousand  three  hundred  and  twenty-five 
Two  thousand  four  hundred  and  thirty-six 

Write  two  thousand  five  hundred  and  forty,  two  thou- 
sand sis  hundred,  two  thousand  and  sixty,  two  thoMsand 
seven  hundred  and  ninety-five,  two  thousand  eight  hundred 
and  fifty,  two  thousand  nine  hundred  and  seventy- seven, 
two  thousand  seven  hundred  and  twenty^seven. 

Read  2037,  2203,  2:^09,  2902,  2092,  2370,  2437,  2307. 

1.  What  cost  4  yards  of  calico,  at  8  cents  a  yard  1 

2.  Wliat  cost  7  quarts  of  chestnuts,  at  5  cents  a  quart? 
8.  Bought  9  dozen  apples,  at  4  cents  a  dozen  ;  'v;hat  did 

tlaey  cost  ? 

4.  I  gave  5  dollars  a  yard  for  G  yards  of  cloth;  what  did 
I  give  for  it  all  ? 

5.  What  should  1  give  for  4  Primary  Arithmetics,  at  9 
cents  apiece  ? 

42 


NOTATION   AND   MULTIILICATION.  §52 


2  51.    Three  thousand 
Three  thoufland  and  three  • 

Three  thousand  and  thirty 
Three  thousand  tliree  hundred 
Three  thousand  three  hundred  and  three 
Three  thousand  three  hundred  and  thirty-throe 
Three  thousand  six  hundred  and  thirty-nine 
Three  thousand  tight  liundnvl  and  twenty-seven 


1*3  denoted 

sooo. 

<( 

3003. 

a 

3030. 

3300. 

'• 

3303. 

333^. 

3039. 

3827. 

Write  three  thousuDd  four  hundred  niid  eighty-seven, 
.three  thousand  five  hundred  and  five,  three  tlior.snnd  and 
seventy,  ihrco  thou.sand  and  nine,  three  thousand  two  hun- 
dred and  ninety-nine,  three  thousand  one  hundred  and 
four,  three  thousand  nine  hundred  and  ninety-nine. 

Read  3456,  3645,  3564,  3465,  3329,  3932,  3093,  3009. 

1.  Laura  bought  4  .^peHing  hooks,   at  10  cents   apiece; 
what  did  the  four  cost? 

2.  James  gathered  7  quarts  of  chestnuts  every  day  for  G 
days  ;  how  many  quarts  had  he  in  all  ? 

3.  Su:^an  bought  5  dresses,  of  9  yards  each  ;    how   many 
yards  were  in  them  all  ? 

4.  Joseph  read  7  chapters  in  the  Bible  every  day   for  a 
week;  how  many  chapters  did  he  read  in  all  1 

5.  Saul  wa.s-sick  7  whole  weeks;   how  many  dayji  was  he 
sick  ? 


?  52.    Four  thousand 

l''our  thousand  and  four 

Four  thousand  aad  ten 

Four  thousand  and  forty 

Four  tkouoaud  five  liundrcd  and  fiJty 
.  Four  tliousand  and  fiity  six 

Four  thousand  and  cighty-uinu 

Four  thousand  seven  liuiylrcd  P.rd  soventy-.six 


is  doioted 

400'), 

" 

4004. 

;( 

4010. 

ii 

4040. 

ti 

.  4550. 

a 

405C. 

i( 

40S9. 

a 

477G. 

V/iitx::  four  thousand  and  nine,  four  thousand  three  liun- 
dred,  four  ihousand  and  seventy^  four  thousand  and  seventy- 
nine,  four  thou.°and  seven  hundred  and  eight,  four  thou- 

43 


S53  PRIMARY   ARITHMETIC. 


sand  three  hundred  and  sis,  four  thousand   one  hundred 
and  one,  four  thousand  seven  hundred  and  seventeen. 
Read  4007.  4014,  4125,  4236,  4247,  4458,  4569,  4670. 

1.  A  man  jj;ave  iiiw  7  children  8  apples  apiece  ;  how  many 
did  lie  ^ive  them  all  ?  . 

2.  If  our  school  fills  8  benches  with  7  girls  on  a  bench, 
how  many  girls  are  there  in  schooH 

o.   Lucy  gave  9  cents  a  yard  for  6  yards  of  calico  ;  how 
much  did  she  give  for  it  all? 


g53.    rire  thoiisand  is  denoted        5000. 

Five  thousand  and  one  "'■  5001. 

Five  thousand  and  eleven  "  5011. 

Five  thousand  and  twehtj'                                              ,     "  5020. 

Five  thousand  one  hundred  "  5100. 

*         Five  thousand  five  hundred  and  fifty  "  5550. 

Five  thousand  and  fifty-five  "  5055. 

Five  thousand  six  hundred  and  eighteen  "  5618. 

Write  five  thousand  three  hundred  and  seventy-five,  five 
thousand  seven  hundred  and  nine,  five  thousand  six  hun- 
dred and  eighty-nine,  five  thousand  seven  hundred  and 
twelve,  five  thousand  three  hundred  and.  forty-eight,  five 
thousand  eight  hundred  atid  seventy. 

Read  5516,  5716,  5671,  5167,  5890,  5089,  5908,  5895. 

1.  Joseph  bought  6  copy-booh.^,  at  10  cents  apiece  ;  what 
did  he  give  for  them  all  ? 

2.  Lawrence  sold  10  quarts  of  blackberries,  at  6  cents  a 
quart ;  what  did  he  receive  for  them  all  ? 

3.  Father  bought  7  yards  of  broadcloth,  at  7  dollars  a 
yard  ;  what  did  it  all  cost  him  ? 

4.  Mother  gave  7  cents  a  dozen  for  9  dozen  eggs;  what 
did  she  give  for  them  all  ? 

5.  Jonathan  bought  5  Primers,  at  11  cents  apiece;  how 
much  did  he  pay  for  them  all  ? 

44 


NOTATION    AND    MULTIPLICATION.  S5'5 


is  denoted 

6000. 

(( 

eooi. 

6006, 

CO-22, 

7103, 

7232. 

7787. 

§54.    Six  thousand 
Six  thousand  and  one 
Six  tliousand  and  six 
Six  thousand  and  twenty-twp 
Seven  thousand  one  hun(h-ed  and  three 
Seven  thousand  two  Inindrcd  and  thirty-two 
Sovon  thousand  ecv6n-hundred  and  eighty-soven 

Write  six  thousand  two  huixdred  and  seventy,  six  thou- 
i^nnd  three  hundred  and  eight,  six  thousand  one  hundred 
nnd  ten,  six  thousand  and  ninety-nine,  seven  thousand  five 
hundred  and  seventy- five,  seven  thousaud  and  seventy, 
seven  thousand  seven  hundred,  seven  thousand  eight  hun- 
dred and  eighty-nine.  t 

Head  0125,  6250,,  6361,  6472,  7132,  7243,  7354,  7465. 

1.  If  7  boys  gather  10  quarts  of  chestnuts  apiece,  how 
many  quarts  do  they  all  gather  1 

2.  Susan  bought  a  calico  dress  containing  0  yards,  at  8 
cents  a  yard ;  what  did  her  dress  cost  ?  . 

3.  Thomas  traveled  8  hours  at  9  miles  an  hour  ;  hov/  far 
did  he  travel  ? 

4.  How  many  persons  are  there  in  10  families,  if  there 
are  7  persons  in  each  ? 


is  denoted 

sooo. 

a 

8008. 

a 

soso. 

a 

ii075. 

a 

9100. 

a 

9201. 

a 

9312. 

f 

•  9423. 

§58.    Eight  thousand 

Eight  thousand  and  eight 

Eight  thousand  and  eighty 

Eight  thousand  and  seventy-five 

Nine  thousand  one  hundiyd 
•   Nine  thousand  two  hundred  and  one 

Nine  thousand  three  hundred  and  twelve 

Nine  thousand  four  hunSred  and  twenty-three 

Write  eight  thousand  one  hundred  and  two,  eight  thou- 
sand two  hundred  and  thirteen,  eight  thousand  three  hun- 
dred and  twenty-four,  eight  thousand  four  hundred  and 
thirty-five,  nine  thousand  five  hundred  and  forty-six,  nine 
thousand  six  hundred  and  fifty-seven,  nine  thousand  seven 

45 


m 


PKIMARY   ARITHMETIC. 


Inindred  and  f-ixty- eight,  cine  thousand  eight  hundred  and 
i^evciity-riine. 

Road  8947,.  883G,  8725,  8G14,  9503,  9492,  9381,  9270. 

1.  If  I  v/ork  9  hours  a 'day  for  9  days^,  how'  many  hoars 
do  I  work  ? 

2.  John  sold  8  quarts  of  ground-peas,  at  10  cents  a  quart; 
what  did  he  receive  for  tl;em  ? 

3.  What  pay  does  a  man  receive  for  10  days'  service,  at 
8  dollars  a  day  '^ 

4.  What  will  9  nionlbs'  board  auiount  to,  at  10  doUars  a 
month  ?  * 

5.  What  cost  10  dozen  Arithmetics,  at  9  dollars  a  dozen  y 


inOtation   and   division 


f;0.    Tea  thousand 
Ten  thousand  and  one 
Ten  thousand  and  ten 
Ten  thousand  one  hundred 
Eleven  thousand 

Twelve  thousand  one  hundred  ^ 

Thirteen  thousand  two  hundred  and  ten 
I'ourteen  thousand  three  hundred  and  tweutj-one 


is  (.u'lioted 


10001. 
»10i)10. 

luioo. 

11000. 
12100. 
13210. 
14321. 


Write  nineteen  thousand  and  ninety -eight,  eighteen  thou- 
sand seven  hundred  and  eighty-seven,  seventeen  thousand 
five  hundred  and  seventy-six,  sixteen  thousand  three  hun- 
dred and  sixty-five,  fifteen  thousand  one  hundred  and  fifty- 
four,  fourteen  thousand  nine  hundred  and  forty>three,  thir- 
teen thousand  seven  hundred  and  thirty-two,,  twelve  thou* 
sand  five  hundred  and  twenty. 

Read  12345,  15878,  10102,  11435,  14768,  17091,  10324. 

1.  At  6  dollars  a  yard,  how  much  cloth  can  be    bought 

for  24  dollars? 
46 


.NOTATION   J^XTi   JjlVL-il 


§57 


■  Model. — The  number  of  yards  it-  c([^t'j]  to  ihc  uwmhcr 
of  times  0  dollars  is  cciitained  171  24  (dollars:  (5  in  24.  4 
times  ;  hence,  4  jards  can  be  bought  for  24  (iOiUir,-\ 

2.  A  lady  divided  21  apples  ccjually  aii)on(r  iun-  7  oImI- 
dren  ;  how  many  apples  did  each  child  receive? 

Model — Each  child  received  one  ^evouth  of  21  apples: 
?>  is  one  seventh  of  21  ,  hence,  each  child  received  3  apples. 

o.  At  8  dollars  a  barrel,  how  niany*barre!s  of  flour  may 
be  bought  for  24  dollars? 

4.  I  spent  27  dollars  for  Latin  Gra!n'Mars,  nt  9  dollars  a 
tlozen  ;  how  many  dozen  did  I  fret  ? 

f).  If  I  give  28  dollars  for  v  cords  of  wood,  how  much  dn 
I  give  per  cord  1 

6.  If  5  barrels  of  corn  c.'st  25  dollars;  ^\hatdoes  1  barrel 
cost  ? 


is  (lonotcJ 

20000. 

a 

20200. 

>t 

22.101. 

.< 

23513. 

(> 

34625. 

" 

35737- 

'• 

G6S49. 

a 

37950. 

257.    Twenty  tbousanci 
TAventy  thousand  two  hnndred 
Twent)'-two  thousand  four  hundred  and  ojie 
Twenty-three  thousand  five  hundred  and  thirteen 
Thirty-four  thousand  six  hundred  and  twenty-five 
Thirty-five  thousand  seven  hundred  and  thirty-seven 
Thirty-six  thousand  eight  hundred  acd  forty-nine 
Thirty-seven  thousand  nine  hundred  and  fifty. 

Write  twenty- nine  thousand  six  hundred  and  forty-five, 
twenty-eight  thousand  five  hundred  and  thirty-four,  twenty- 
.seven  thousand  three  hundred  and  twelve,  twenty-five  thou.- 
sand  one  hundred  and  ninety,  thirty-six  thousand  two  hun- 
dred and  ten,  thirty-four  thousand  and  ninety-five,  thirty- 
three  thousand  nine  "hundred  and  seven ty-t^ree,  thirty-one 
thousand  seven  hundred  and  fifty- one. 

Read  20125,  21286,  22347,  23458,  35469,  36570,  37681, 
38792,  34975,  37384. 

1.  At  10  cents  apiece,  how  many  oranges  can  you  buy 
for  40  cents  ? 

47 


§58  PRIMARY   ARITHMETIC. 


2.  At  8  cents  a  yurd,  how  many  yards  of  calico  can  you^ 
buy  for  40  cents'? 

3.  At  5  miles  an  hour,  hoar  long  will   it  take  to   go  35' 

miles? 

4.  At*  4  dollars  a  cord,  how  many  cords  of  wood  can  you 
buy  for  32  dollars  ? 

5.  At  9  dollars  a  month,  how  long  could  you  board  for 
36  dollars  ? 


§58.,   Forty  thousand  is  denoted        40000. 

Forty  thousand  and  forty  "  40040. 

Forty  thousand  four  hundred  "  40400. 

Forty-four  thousand  and  four                       .  "  44004. 

Fifty  tliousand  one  hundred  and  five                    ■  ''  50105. 

Fifty-one  thousand  two  hundred  and  sixteen  "  51216. 

Fifty-two  thousand  tliree  hundred  and  twenty-seven  "  '         52327. 

Fifty-four  thousand  five  hundred  and  forty-nine.  "  64549. 

Write  forty  thousand  three  hundred  and  twenty  one,, 
forty-three  thousand  six  hundred  and  fifty-four,  forty-six 
thousand  nine  hundred  and  eighty- seven,  forty-nine  thou- 
sand two  hundred  and  ten,  fifty-two  thousand  five  hundred 
and  forty-three,  fifty-five  thousand  eight  hundred  and  sev- 
enty-six, fifty-eight  thousand  one  hundred  and  nine,  fifty- 
one  thousand  four  hundred  and  thirty-two. 

Read  41482,  44765,  47098,  40321,  53656,  56987,  59210. 

1.  How  long  would  it  take  to  travel  40  miles,  at  5  miles 
an  hour  ? 

2.  How  many  yards  of  broadcloth,  at  9  dollars  a  yard,, 
may  be  bought  f^r  45  dollars? 

3.  If  7  cords  of  wood  cost  42  dollars,  what  does  1  cord 
cost? 

4.  If  6  Spelling  Books  cost  48  cents,  what  does  one  cost?' 

5.  If  a  boy  divides  49  apples  equally  among  his  7  class- 
mates, how  many  does  he  give  them  each  ? 

48^ 


POTATION   AND   DIVISION* 


§60 


ii5  denoted 

GOOOO.   ■ 

li 

62000. 

n 

64100. 

a 

C632Q. 

" 

78543. 

'• 

70765. 

a 

72987. 

a 

741C9. 

g59.     Sixtj'^  thouj^and 
Sixtj'-two  thousand 
Sixty-four  thousand  ono  hundred 
Sixty-six  thousand  three  hundred  and  twenty 
Seventy-eight  thousand  five  hundred  and  forty-three 
Seventy  thousand  scveu  hundred  and  sixty-five   - 
Sevonty-two  thousand  nine  hundred  and  eighty-seven 
Seventy-four  thousand  ono  htmdred  and  nine 

Write  sixty-five  thousand  four  hundred  and  thirty-two, 
sixty-six  thousand  five  hundred  and  forty-three,  sixty-seven 
thousand  six  hundred  and  fifty-four,  sixty-eight  thousand 
seven  hundred  and  sixty-five,  aeventy-nipe  thousand  eight 
hundred  and  seventy-six,  seventy  thousand  nine  hundred 
and  eighty-seven,  sevfenty-one  thousand  and  ninety-eight, 
seventy- two  thousand  one  hun^dred  and  nine. 

Read  6357D,  64680,  66802,  a7913,  78024,  79135,  70246V 

1.  Sallie  gave  50  cents  to  10  poor  children  equally  •  how 
much  did  she  give  them  apiece  ? 

2.  A  school  of  54  girls  is  divided  into  6  equal  classes  •. 
how  many  girls  are  in  each  class  ? 

3.  A  farmer  made  56  bushels  of  corn  from  7  eq^al'rowfi^, 
how  many  bushels  did  he  make  from  each  row  ? 

4.  If  8  boys  gather  56  quarts  of  hazel  nuts,  how  many 
quarts  does  each  boy  gather  ? 


§60.    Eighty  thousand  * 

Eighty-two  thousand  and  two 
Eighty-four  thousand  ono  hundred  and  six. 
Eighty-six  thousand  and  twenty-eight 
Ninety-seven  thousand  three  hundred  and  forty. 
Ninety-nine  thousand  five  hundred  and  sixty-on© 
Ninety-five  thousand  six  hundred  and  nineteen 
Ninety-six  thousand  one  hundred  and  ninety-ftvo. 

Write  eighty-one  thousand  two"  hundred  and  five,  eighty- 
three  thousand  and  fifty-one,  eighty  thousand  five  hundred 
and  thirteen,  eighty-five  thousand  one  hundred  and  thirty, 
ninety-six  thousand  two  hundred  and  forty-one,  ninety-two 
49  D 


ia  denoted 

80000. 

a 

82002. 

a 

84106. 

ii. 

SC028. 

(i: 

97340. 

«' 

99561. 

'- 

95619.' 

ii 

96195. 

§60  PRIM AE.Y   ARITHMETIC. 

thousand  four  hundred  and  sixteen^,  ninety-four  thousand 
one  hundred  and  sixty-two,  ninety-one  thousand  six  hun- 
dred and  twenty-four. 

Kead  80246,  82460,  84602,  86024,  97135,  91357,  93571. 

1.  At  6  shillings  a  bushel,  how  many  bushels  of  apples 
can  be  bought  for  60  shillings  ? 

2.  At  7  shillings  a  yard,  how  many  yards  of  cloth  can  be 
bought  for  63  shillings  ? 

3.  At  8  cents  a  yard,  how  many  yards  of  •ribbon  can  be 
bought  for  64  cents  ? 

4.  If  a  father  divide  70  marbles  equally  among  his  7  sons, 
•how  many  marbles  will  each  receive  ? 

5.  If  a  gallon  of  milk  cost  9  cents,  what  number  of  gal- 
lons will  cost  72  cents  ? 

6.  A  planter  wishes  to  make  10  equal  fields  to  contain  80 
acres  in  all ;  how  many  acres  will  each  field  contain  1 

7.  His  neighbor  wishes  to  divide  81  acres  into  fields  of. 
9  acres  each  ;  how  many  fields  will  he  have  ? 

8.  At  10  cents  apiece,  how  many  lead  pencils  can  you 
buy  for  90  cents  ? 

50 


PART    III. 


WEITTEN   ARITHMETIC. 

NOTATION. 

§  61.     Aritlimetic  is  the  science  of  numbers. 
§  62.     A  unit  is  any  single  thing. 
§  (33.     A  number  is  a  collection  of  units. 
§  64.     Numbers  are  denoted  bj  figures.     For  this  pur- 
pose  the  following  ten  figures  are  used  :    0  naught,  1  one 
2  two,  3  three,  4  four,  5  five,  G  six,  7  seven,  8  eight,  9  nine! 
^  The  figure  0  is  used  simply  to  fill  vacant  places,  and  is 
aiways  omitted  in  reading. 
§  6'5.     10  units  make  1  ten, 

1^  *^^s  "       1  hundred, 

10  hundreds  «       1  thousand, 

10  th6usands  «       1  ten-thousand, 

10  ten-thousands  ^*       1  hundred-thousand, 

10  hundred-thousands    "  '    1  million 
10  millions  u       1  ten-million, 

10  ten.millions  "       i  hundred-million, 

10  hundred-millions      «      1  billion,  &c. 
51 


\6S  PRIMARY   ARITEMETICr. 


»  A  unit  is  called  a  unit  of  the  first  order, 

A:  ten    .  "       a  unit  of  the  second  order, 

A  hundred  *'       a  unit  of  the  third  order, 

A  thousand  "       a  unit  of  the  fourth  order,. 

A  ten-thousand  "       a  unit  of  the  fifth  order, 

A  hundred-jbhousand        "       a  unit  of  the,sixth  order,  &c. 

Thus,  ten  units  of  any  or'^er  make  one  of  the  next  higher. 

§  66.  Any  number  less  than  ten  is  denoted  by  one  fig- 
ure, as  in  §  04. 

§  67.     To  denote  a  number  between  nine  and  one  hun- 
dred, two  figures  are  placed  side  by  ri^e,   the   one  on  the' 
right  denoting  simple  units,  and  the  "fher  denoting  tens. 

Thus,  twenty-one,  (that  is,  two  tens  aud  one  unit),  is  de- 
noted 21 ;  thirty-two  is  denoted  S2 ;  forty-three  43  ;  fifty- 
four  54  •  sixty -five  65  ;  seventy-six  76  ;  eighty-seven  87. 

In  23,  how  many  units,  and  how  many  tens  t  How  many 
of  each  in  29?  In  34?  In  45  ?  In  50  ?  In  61  ?  In  16  ? 
In23?    In  49?    In94?.In86?    In  68  ?    In  40  ?    In  27  ? 

Read  14,  25,  52,  3&,  63,  10,  26,  62,  37,  73,  25,  53,  3(>, 
64,  47,  75,  58,  86,  69,  97,  78,  86,  67,  56,  45. 

Write  seventeen,  twenty-six^  thirty-five,  forty- six,  fifty- 
five,  sixty-four,  seventy-three,  eighty-two,  ninety-eighty 
seventy-one,  .sixty-two,  fifty-three,  forty-four,  thirty-four, 
twenty-five,  thirty-six,  eighteen,  nineteen,  ninety, 

§  68.  .To  denote  a  number  between  ninety-nine  and  one 
thousand,  three  figures  are  placed  side  by  side,  the  one  on- 
the  right  denoting  units,  the  next  denoting  tens,  and  the 
other  denoting  hundreds. 

Thus,  five  hundred  and  twenty-six,  (that  is,  five  hun- 
dreds, two  tens,  and  six  units),  is  denoted  526 ;  one  hun- 
dred and  twenity-three  is  denoted  123  ;  two  hundred  and 
thirty-one  231 ,  three  hundred  and  twelve  312. 

52 


NOTATION. 


In  127,  liow  maDy  units,  how  many  tens,  und  how  many 
hundreds?  How  many  of  each  in  271  ?  In  7121  In  172? 
In  246?  In  357?  In  579  ?  In  480?  In  591  ?  In  602? 
In  369  ?     In  470  ?     In  259  ?     In  350  ?     In  503  ?    In  507  ? 

Read  147,  238,  367,  478,  589,  690,  701,  812,  923,  134, 
245,  358,  467,  578,  689,  790,  801,  912,  129,  230,  341,  452, 
563,  674,  785,  896,  907,  108,  219,  320,  435. 

Write  2  hundreds  and  4  tens,  3  hundreds  and  5  units,  4 
hundreds  1  ten  and  6  units,  5  hundreds  2  tens  and  8  units, 
6  hundreds  3  tens  and  9  units,  7  hundreds  and  4  tens,  8 
hundreds  and  5  units. 

Write  4  units  of  the  1st  order  and  5  of  the  3rd ;  3  units 
of  the  2nd  order  and^4  of  the  3rd  ;  7  units  of  the, 1st  order, 
^  of  the  2nd,  and  5  of  the  3rd  ;  G  units  of  the  Srd.  order,  4 
of  the  2nd,  and  S  of  the  1st ;  2  units  of  the  3rd  order  .and 
9  of  the  2nd  ;  8  units  of  the  3rd  order  and  4  of  the  1st.* 

Write  one  hundred  and  twenty-seven,  two  'hundred  and 
thirty-eight,  three  hundred  and  forty-nine,  foiir  hundred 
and  sixty,  five  hundred  a»d  se-^ienty-one,  {?ix  hundred  and 
eighty-two,  seven  hundred  and  ninety -three,  eight  hundred 
and  four,  nine  hundred  and  fifteen. 

§  69.  To  denote  a  number  larger  than  999,  more  than 
three  figures  are  used  ;  and  these  figures  are  separated  into 
periods  of  three  figures  each,  beginning  at  the  right. 

§  70.  The  names  of  the  periods  in  their  order  frogi  right 
to  left  are  as 'follows :  1st,  units;  2nd,  thousands;  3rd. 
•millions;  4th,  billions  ;  5th',  trillions ;  6th,  quadrillions,* 
7th,  quintiilions;  8th,  sextillions;  9th,  seplillions ;  10th. 
octillions,  &c. 

§  71.  In  each  period,  the  figure  on  the  right  denotes 
units,  the  next  tens,  and  the  other  hundreds,  of  that  period. 

Thus,  123  in  the  2nd  period  denotes  one  hundred  and 
53 


§72 


PRIMARY   ARITHMETIC- 


twenty-three  thousand  ;  245  in  the  3rd  period  denotes  two 
hundred  and  forty-five  millions  ;  102  in  the  4th  period  de- 
notes one  hundrgi  and  two  billions. 

§72.  The  1st,  2nd5  and  3rd  orders  constitute  the.  Isfc 
period  ;  the  4th,  5th,  and  6th  orders  constitute  the  2nd 
period;  the  7th,  8th,  and  9th  orders  consbitute  the  3rd 
period,  &c. 


§  73.  1000  units 

make 

1  thousand, 

1000  thousands 

i( 

1  million. 

1000  millions 

a 

1  billion, 

1000  billions 

iC 

1  trillion, 

1000  trillions 

>£ 

1  quadrillion, 

1000  quadrillions 

k  i 

1  quintillion. 

Thus,  one  thousand  units  of  any  period  make  one  of  the 
next  higher. 

§  74.  Rule  for  Reading  NuxMbers. — Sepanite  the  fi'j- 
ures  into  periods  of  three  figures  each,  beginning  at  the 
right ;  then,  beginning  at  the  left.  ?-^';  ?  each  'period  as  if  it 
stood  alone,  and  pronounce  the  nuuie  of  the  period  after 
reading  it.  * 

Read  the  following  numbers  -. 


•3462 

9077 

5435- 

6428 

4005 

8611 

J  776 

1864 

'  26408 

31597 

72410 

47400 

98780 

40862 

57913 

42701 

109875 

151903 

168024 

753812 

210986 

382014 

409135 

864923 

1421097 

44i)3125 

5510246 

7975034 

7142109 

5449312 

6551024 

4797503 

19012417 

21394455 

54301556 

43057974 

20123529 

32405467 

65312605 

54168085 

20345630 

976453240 

653126075 

541680854 

12034563 

197615325 
54 

165311565 

5416808540 

NOTATION.  §74 


Write  the  following  numbers  in  figures  : 

49.  Six  thousand,  four  hundred  and  eight. 

50.  Seventy  thousand,  and  twenty-eight. 

51.  Eight  hundred  and  fifty-one  thousand,  nine  hundred 
and, fifty-two. 

52.  Nine  millions,  eighty-one  thousand,  an(!f  ninety. 

53.  Sixty-three    millions,   twenty-seven   thousand,    five 
hundred  and  twenty -five. 

54.  Four  hundred  millions,  and  four. 

55.  Three  millions,  three  thousand,  and  three. 

56.  Twenty  millions,  twenty  thousand,  and  twenty. 

67.  One  hundred  millions,  one  hundred  thousand,   one 
hundred. 

58.  Two  billions,  three  millions,  four  thousand,  and  five. 

59.  Sixty  billions,  seventy  millions,  eighty  thousand,  and 
ninety. 

60.  Six  hundred  billions,  eighty  millions,  ten  thousand, 
and  nine. 

"61.  Seventy-five  billions,  seventy-five  thousand. 

62.  Ten  billions,  one  hundred  millions,  and  one. 

63.  Twenty-nine  billions,  and  ninety-nine. 

64.  Six  hundred  and  fifty  billions,  forty-three  millions, 
twenty-one  thousand,  nine  hundred  and  eighty-five. 

65.  Seventy-nine  trillions,  seven  hundsed  and  seven  mil- 
lions, eight  hundred  and  eighty. 

Write,  and  then  read,  the  following  :  • 

QQ.  25  units  of  the  1st  period,  75  of  the  2nd,  and  10  of 
the  3rd. 

67.  17  units  of  the  2nd  period  and  23  of  the  3rd. 

68.  175  units  of  the  3rd  period  and  715  of  the  1st. 

69.  225  units  of  the  1st  period  and  25  .of  the  4th. 

70.  23  units  of  the  1st  period  and  225  of  the  3rd. 

55 


§75  PRIMARY   ARITHMETIC. 

71.  321  units  of  the  3rd  period,  32  of  the  2nd,  and  H  of 
the  1st. 

72.  123  units  of  the  1st  period,  45  of  the  3rd,  and  6  of 
the  5th. 

73.  7  units  of  the  1st  period,  8  of  the  2nd, -90  of  the  3rd, 
and  100  of  tUe  4th. 

74.  230  units  of  the  4th  period,  45  of  the  3rd,  and  19  of 
the  1st. 

75.  25  in  the  period  of  units,  3  in  that  of  thousands,  47 
of  millions,  and  127  of  trillions. 

76.  135  in  the  period   of  quadrillions,  790  of  billions, 
and  59  of  thousands. 

77.  264  in  the  period  of  trillions,  80  of  millions,  and  68 
of  units. 

78.  147  in  the  period  of  billions,  25  .  : 
•  thousands,  and  40  of  units. 

79.  400  in  the  period  of  millions,  40  of  thousands,  aad 
4  of  units. 

Note. — Let   the  teacher  extend  suck  exercises  until  the  class 
seem  to  be  perfectly  familiar  with  tiio  principles  of  Notation. 


•     •    ADDITION. 

§  75.  *Addition  is  the  operation  of  jB.ndiDg  one  number 
equal  to  several  other  numbers  put  together. 

§76.  The  result  of  addition  is  called  .the  sum  of  the 
numbers  added.  Thus,  10  is  the  sum  oi  6  and  4,  because 
10  is  equal  to  6  and  4  put  together. 

Before  proceeding'  further,  let  the  pupil  thoroughly 
memorize  the  following  Table. 

56  • 


ADDITION. 


§78 


J\.13I31TION    T:_4lI3LE:. 


2  nnd  0  are 
2  and  1  .".re 
2  and  2  are 
2  and  3  are 
2  and  4  are 
2  t.nd  5  are 
2  and  6  are 
2  and  7  are 
2  and  8  arc  10 
2  and  9  are  11 


f?  and 
3  and 
3  and 
3  and 
3  and 
3.  and 
3  and 
3  and 
3  and 
3  and 


0  nrc 

3 

1  are 

4 

2  arc 

5 

3  are 

6 

4  are 

7 

5  arc 

8 

G  are 

9 

7  are 

10 

8  are 

11 

9  are 

12 

n 

4  and  0  afe 
4  and  1  are 
4  and  2  are 
4  and  3  are 
4  and  4  are 
4  and  5  are 
4  and  6  are 
4  and  7  are 
4  and  8  arc 


4 

5 
(S 
7 
8 
9 
10 
11 


4  and  9  are  13 


5  and  0  are  5 

5  and  1  nve  '*> 

5  and  2  arc  7 

5  and  3  are  8 

5  and  4  are  9 

5  and  5  are  10 

5  and  6  are  11 

5  and  7  are  12 

f)  and  8  are  13 

r^  and  9  arc  14 


6  and  0 
6  and  1 
6  and  Q 
6  and  8 
6  and  4 
G  and  5 
G  and  0 
6  and  1 
G  and  S 
G  and  9 


are 

6 

are 

7 

are 

8 

are 

9 

are 

10 

are 

11 

are 

12 

are 

13 

are 

14 

arc 

15 

7  and 
7  and 
7  and 
7  and 
7  and 
7  and 
7  and 
7  and 
7  and 
7  and 


0  are 

1  are 

2  a^e 
8  are 

4  are 

5  are 

6  are 

7  are 

8  arc 

9  are 


8 
9 
10 
11 
12 
13 
14 
15 
16 


8  and 
8  and 
8  and 
8  and 
8  and 
8  and 
S  and' 
8  and 
8  and 
8  and 


0  are 

1  are 
iiare 

3  are 

4  are 

5  are 
G  are 

7  are 

8  are 

9  are 


10 
11 
12 
13 
14 
15 
16 
17 


9  and  0 
9  and  1 
9  and  2 
9  and  3 
9  and  4 
9  and  5 
9  and  G 
9  and  7 
9  and  8 
9  and  9 


arc  9 
are  10 
are  '11 
are  12 
are  13 
are  14 
are  15 
are  16 
are  17 
are  18 


§  77.  Two  or  more  numbers  can  not  be  added  "or  put 
together,  unless  they  are  similar.  We  can  not  say  that  2 
apples  and  3  peaches  make  5  a^pples  or  5  peaches.  So,  4 
dollars  and  5  cents  make  neither  9  dollars  nor  9  cents.  In 
the  sanie  way,  2  simple  units  and  6  tens  make  neither  8 
units  nor  8  tens. 

Ex.  1.  Add  2,  3,  and  4. 

9 

-J  • 

3  §  78.     MoDEL.^4  and  3  are  7,  and  .2  are  9. 

•  4         The  sum  is  9'. 

•  9 

Explanation. — These  three  numbers  can  evidently  be 
added  together,  because  each  of  them  is  some  number  of 
•     '        57  •  ■ 


§79  PRIMARY   ARITHMETIC. 


Simple  units,  and  henee  they  are  all  similar.  Beginning 
afc  the  foot  of  the  column  in  which  they  are  arranged,  and 
going  up  itj  as  in  the  Model,  we  readily  find  that  9  is  equal 
to  the  three  numbers  pat  together  :  and  henoo  V7^  GODclude 
that  their  sum  is  9. 

Note. — Let  the  teacheT  seo  (.o  it  that  the  pupil  recites  prf  cisely 
according  to  the  mode!  both  here  and  wherever  a  model  is  given. 

Ex.  2.  Add  1,  3,  and  5.  '                Sum,  9. 

3.  What  is  the  sum  of  Ij  2,  and  8  ?  Ans.  6. 

4.  What  is  the  sum  of  2,  3,  and  2  ]  ,  Ans.  7. 

5.  Find  the  sum  of  1,  3,  i*id  4.  Sum,  8. 

6.  Find  the  sum  of  2,  4,  and  2.  -     Sum,  8. 
.  7.  Add  10,  20,  and  40. 

10     • 

20  §  79.     Model. — 0  ;  4  and  2  are  G,  and  1  are 

40         7.     The  sum  is  70. 
70 
Explanation. — Since  each  of  these  numbers  is  a  num- 
ber of  tens,  they  can  be  added  together.     The  0  is  written 
at  the  right,  to  keep  the  7  in  its  proper  place,  v.. 

Ex.  8.  Add  10,  50,  and  20.        .  >Sum,  80. 

.  9.  What  is  the  sum  of  30,  20,  and  10  ?  Ans.  (50. 

10.  What  is  the  sum  of  3Q,  20,  and  20  ?  Ans.  70. 

11.  Find  the  sum  of  40,  30,  and  10.  Sum,  80. 

12.  Find  the  sum  of  40,  20,  a^nd  20.  Sum,  80. 

13.  Add  together  23  aiid  84. 

2^  §80..    Model.— 4  and  3  are  7.^  8  and  2  are 

51         5.     The  sum  is  57. 
57 
Explanation. — Each  of  these  numbers  consists  partly 
of  units  and  partly  of,  tens.     The  units  and  the  tens  can 
not  be  added  all  togetlier,  as  we  learned  in  §  77 ;   but  the 
-      58 


ADDITION.  S81 


units  can  be  added  together  in  one  sum,  and  the  tens  in  an 
other,  and  these'two  sums  may  be  placed  side  by  side,  each 
in  i'js  proper  place.  By  this  means  the  two  given" numbers 
arc  added  together.  The  numbers  are  arranged  for  con- 
venience with  units  under  units,  and  tens  under  tens. 

la  like  manner,  numbers  expressed  by  more  than  two 
figures  may  be"  added  by  taking  the  sum  of  the  nnit;^,  tlien 
the  sum  of  the  tens,  and  then  the  sum  of  the  hundreds,  &c., 
from  rio-ht  to  left. 

Ex.  14.  Add  together  123,  231,  and  115.  Sum,  469. 

15.  Add  1023,  2031,  and  1105..  Sum,  4159. 

16.  Find  the  sum  of  113.402  and  5321 J5.     Sum,  655527. 

17.  Find  the  sum  of  10321,  34102,  and  12321. 

18.  What  is  the  sum  of  2742,  1034,  and  4211  ?• 

19.  Add  123,  456,  and  633.  •  . 

]'-^^  §81.     Model.— 3  and  6  are  9,  and  3  are 

12  ;  1  and  3  are  4,  and  5  are  9,  and  2  are  11 ; 
1  and.  6  are  7,  and  4  aro  11,  and   1   are  12. 


456 
633 


1212         The  sum  is  1212. 

Explanation. — After  arranging  the  numbers  as  in  §80, 
v/e  find  the  sum  of  the  column  of  units  to  be 
123  12  units.  Sine:;  this  is  expressed  by  two  fig- 
456  ures,  it  can  not  be  placed  under  that  column. 
633  We  may,  however,  place  2  under  the  column 
]2  of  unit?,  and  1  on  its  left,  or  under  the  col- 
10  umn  o1^tcD.«.     It  v/e  add  the  column  of  tens, 

]X  we  find  10  tens  for  its  sum;  and  this  can  not 

Y^-pj  be  placed  under  the  column  of  tens,  for  the 
"''■'"'  same  reason  :  but  we  may  place  the  0  under 
the  tens,  and  the  1  on  its  left,  or  under  the 
hundreds.  In  like  mann-jr,  the  11  hundreds,  which  we  get 
fi'oifL  the  third  column,  may  be  written  partly  under  hun- 
dreds and  partly  still  further  left.  By  adding  these  partial 
sumS;  we  obtain  1212,  the  same  as  in  the  Model. 

In  pracfcicQ  it  is'unnecessarv  to  write  the  several  partial 
59 


mi 


PRIMARY   ARITHMETIC. 


BUD.1S  in  tliio  way,  if  we  are  careful  to  add  the  left  hand  fig- 
ure of  eacli  partial  sum  to  the  numbers  in  Ihe  next  column 
on  the  left.     In  the  Model,  this  figure  is  taken   in  first  in    ^ 
adding,  for  fear  of  its  beiitg  forgotten. 
We  may  now  give  the  following 

Rule  fo&  Addition. —  Arrange  the  numhcrs  iclth  units 
of  the  mme  order  in  the  same  column. 

Beginning  at  the  right,  find  the  sutn  of  each  column  ;  if 
this  sum  is  exjjressed  hy  one  figure^  set  it  doion  under  flic 
cilamn  f  hiU^  if  it  is  expressed  hy  more  thiin  one  figure^  yet 
the  "right  hand  figure  imd^r  this  column^  and  add  the  re- 
inaining  figure  or  figures  in  loith  the  next  cohiinu. 

JSet  down  the  whole  sum  of  the  If  st  col(i77i7i. 

PiiooF.* — 1.  Add  as  before,  but  begin  at  the  top  of  eacli 
column. 

Or,  2.  Find  the  sum  of  all  the  numbers  but  one,  and  ^o 
this  sum  add  the  number  excepted. 


Ex.  21.  Add  246,  157,  and  290. 

22.  Add  1234,  4507,  and  1752. 

23.  Add  2461,  5729,  and  1207. 

24.  Add  1864,  8641,  and  4681. 

25.  Add  1864,  18645,  and  186456. 
2Q.   Add  1G23,  10234,  and  102349. . 
37.  Add  1020,  30405,  and  607080. 

28.  Adda234,  5678,  and  90807. 

29.  Add  13057,  12304,  and  10509." 

30.  Add  27903,  72903,  and  30927. 

31.  What  is  the  sum  of  38014,  83014, 

32.  What  is  the  sum  of  ,49125,  52149, 


Sum,  693j 


Sum. 


,  7493. 

Sum,  9397. 

Sum,  15186, 

Sum,  206965. 

Sum,  113606. 

Sum,  638505. 

Sum,  97719. 

Sum,  35870. 

Sum,  131733. 

and  41838  ?  «  . 

Ans.  162866. 

and  51949? 

An*.  153223, 


ADDITION.  §81 


33.  What  is  the  sum  of  53236,  63254,  and  02051  ? 

Alls.  178541. 

34.  What  h  the  sum  of  63307,  74365,  and  73162  ? 

Ans.  21083-1, 
36.  What  is  the  sum  of  75418,  85476,  and  84273  ? 

Ans.  245167, 

36.  What  is  the  sura  of  86529,  96587,  and  95384  ? 

Ans.  278500. 

37.  What  is  the  sum  of  97630,  70698,  nn^l  60495  ? 

Ans.  228823. 

38.  What  is  the  sum  of  80741,  81709,  and  70506  '^     ■ 

Ans.  232956. 

39.  What  is  the  sum  of  91852,  92810,  and  81617  ? 

'  .  Ans.  266279. 

.   40.  What  is  the  sum  of  302983,  92728,  und  3921  ? 

Ads.  399612, 

41.  Find  the  sum  of  413074,  103829,  and  31032. 

Sum,  547935. 

42.  Find  the  sum  of  513185,  2149310,  31145,  and  42143. 

Sum,  2735783. 

43.  Find  the  sum  of  U23295,  32510421, 43256,  and  53254. 

Sum,  33230226. 

44.  Find  the  sum  of  7345106,  43621532,  54367,  and 
64375  Sum,  51085380. 

45.  Find  the.sum  of  8457216,  54732043,  65478,  and 
75386.  Sum,  63330723, 

46.  Find  the  sum  of  9568327,  65843754,  75689,  and 
86497.  Sum,  75^74267. 

47.  Find  the  sum  of  10679438,  76954865,  867910,  and 
975108.         *  Sum,  89477321. 

48.  Find  the  sum  of  217810549,  871065976,  9781021, 
and  1086219.  Sum,  1099743765. 
•  49.  Add  3189216510,  982176087,  10892132,  and 
21973210.                    Sum,  13043842939. 

61 


PRIMARY   ARITHMETIC. 


50.  Add  4291032, 76211003, 2872198, 20910324,332108, 
and  431194321.  Sum,  535811076. 

51'.  Add  5926873,  3927591,  4389217,  6431279,  3326981, 
and  5678901.  Sam,  29680842. 

52.  Add  20065321,  67754826,  83332716,  2176534498, 
and  3222110097.  Sum,  5569796958. 

53.  Add  327,  916,  424,  326,  917,  ISO,  232,  316,  419, 
550,  613,  222,  and  311.  Sum,  6693. 

54.  Add  2160,  6120,  1260,  1620,  2610,  1234,  4321, 
1200,  1020,  3156,  and  2150.  Sum,  26S51. 

55.  Add  2175,  1750,  2318,  9129,  6312^  2120,  3816. 
4505,  3216,  7888,  and  3200.  Sum,  46429, 

56.  Add  36,  22,  20,  19,  43,  16,  and  10.     Sum,  166. 

57.  Add  50,  60,  70,  81,  18,  91,  and  i9.     Sum,  389, 


-«<5»- 


SUBTRACTION. 

§82.  Subtraction  is  the  operation  of  finding  the  differ- 
ence between  two  numbers,  by  taking  tlie  less  from  the 
greater. 

§83.  The  number  to  he  subtracted  is  called  the  subtra- 
hend. 

§  84. '  The  number  to  be  diminished'  is  called  the  minu- 
end, 

§  85.  The  result  of  subtraction  is  called  the  remainder 
or  the  difference. 

Before  proceeding  further,  let  the  pupil  thoroughly? 
memorize  the  following  Table. 

62 


SUBTRACTION, 


sujsxn^vcxioi^  x..-^sL"ii:. 


1  from 
1  from 
from 
from 
fi^m 
from 
from 
from 


1  from 
1  from 


1  leaves  0 

2  leavog  1 

3  leaves  2 

4  leaves  3 

5  leaves  4 

6  leaves  5 

7  leaves  6 

8  leaves  7 

9  leaves  8 
10  leaves  9 


2  from 
2  from 
2  from 
2  fi'om 
2  from 
2  from 
2  from 
2^  from 
2  from 
2  from 


2  loaves  0 

3  leaves  1 

4  leaves  2 

5  leaves  8 

6  leaves  4 

7  leaves  6 

8  leaves  G 
i>  leaves  7 

10  leavep  8 

11  leaws  0 


3  from 
S  from 
3  from 
8  from 
3  from 
3  from 
.3  from 
3  from 
3  from 
8  from 


3  lenvfs  0 

4  leaves   1 

6  loaves  2 
0  leaves  3 

7  leav<is  4 

8  loaves  5 
0  leaves  G 

10  leaves  7 

11  leaver  8 

12  leaves  0 


4  from 

4  leaves  0 

5  from 

5  leaves  0 

G  from 

G  leaver 

0 

4  from 

5  leaves  1 

5  from 

G  leaves  1 

G  from 

7  leaves 

] 

4  from 

6  leaves  2 

5  from 

7  leaves  2 

G  from 

8  leaves 

•  ■) 

4  from 

7  leaves  3 

5  from 

8  leaves  3 

G  from 

9  leaves 

3 

4  from 

8  leaves  4 

5  from 

9  leaves  4 

6  from 

10  leaves 

4 

4  from 

9  leaves  5 

5  from 

10  leaves  5 

G  from 

11  leaves 

5 

4  from 

10  leaves  G 

5  from 

1 1  leaves  G 

6  from 

12  leaves 

G 

4  from 

11  leaves  7 

5  from 

4.2  leaves  7 

G  fi-om 

'13  leaves 

7 

4  from 

12  leaves  8 

5  from 

13  leaves  8 

G  from 

14  leaves 

8 

4  from 

13  leaves  9 

5  from 

14  loaves  9 

G  from 

15  leaves 

9 

from 
from 
from 
from 
from 
from 
from 
from 
from 
from 


7  leaves  0 

8  leaves  1 

9  leaves  2 

10  leaves  3 

11  leaves  4 

12  leaves  5 

13  leaves  6 

14  leaves  7 

15  leaves  8 

16  leaves  9 


8  from 
8  from 
>  8  from 
8  from 
8  from 
8  from 
8  from 
8  from 
8  from 
8  from 


8  leaves  0 

9  leaves  1 

10  leaves  2 

11  leaves  3 

12  leaves  4 

13  leaves  5 

14  leaves  6 

15  leaves  7 

16  leaves  8 

17  leaves  9 


9  from 
9  from 
9  from 
0  from 
9  from 
9  from 
9  from 
9  from 
9  from 
9  from 


9  leaves 

10  leaves 

11  leaves 

12  leaves 
18  leaves 

14  leaves 

15  loaves 
IG  leaves 

17  leaves 

18  leaves 


§  86.     The  difference  between  two  numbers  can  not  be 

found,  unless  they  are  similar.     We   can  not  say  that  2 

apples  from  5  peaches  leaves  3  apples  or  3  peaches.     So,  5 

cents  from  7  dollars  leaves  neither  2  cents  nor  2  dollars. 
63 


PRIMARY   ARlTIlMEIlC. 


In  the  same  way,  3  simple  units  from  7  tens  leaves  neither 
4  units  nor  4  tens.  % 

§  87.  The  difference  between  two  numbers  is  not  changed 
by  increasing  those  numbers  equall}^     Thus, 

The  difference  between  8  and  3  is  5 :  now,  add  4  to  each 
of  these  numbers,  and  the  difference  between  12  and  7  is  5 
still:  again,  add  6  to  each  of  these  last,  and  the  differo^ice 
betvv'cen  18  and  13  is  5  still  :  and  so  on.        - 

Ex.  1.  Subtract  25  from  48. 
•     48 

25  .  §  88.     MoDSL.— 5  from  8  leaves  3  :  2  from  4 

23  leaves  2.     The  remainder  is  23. 

Explanation. 7— We  arrange  the,  two  numbers  with  units 
under  units^  and  tens  under  tens,  placing  the  subtrahend 
under  the  minuend.  We  then  take  the  .units  of  the  sub- 
trahend from  those  of  the  minuend,  leaving  3  units  for  the 
remainder^;  and  we  then  take  tfiie  tens  of  the  subtrahend 
from  those  of  the  minuend,  leaving  2  tens  for  the  remainder. 

In  the  same  way  we  would  proceed  if  the  numbers  were 
composed  of  more  than  two  figures  each,  taking  the  differ- 
ence ;  first  of  the  units,  next  of  the  tens,  then  of  the  hun- 
dreds, &c.,  from  right  to  left. 

Ex.  2.  Subtract  123  from  369.  Rem.  246. 

3.  Subtract  1024  from  2158.  Rem.  1134. 

4.  Subtract  1203  from  7894.  Rem.  6691. 

5.  Subtract  2345  from  5689.  Rem.  3344. 

6.  From  98575  take  34543.  .        Rem.  64032. 

7.  From  575898  take  364032.  Rem.  211866. 

8.  From  568759  take  203203.  cRem.  365556. 

9.  From  679868  take  1^2302.  Rem.  5775G6. 
■     10.  From  789977  take  123456.                     Rem.  666531, 

11.  From  2561  take  836. 
64 


SUBTRACTlOx\.  §{)0 


^5G1  §89.     Model.— G  from  11  leaves  5;    .4 

836         from  G  leaves  2  ;  8  from  15  leaves  7;   1  from 
1725         2  leaves  1.     The  reuiaiuder  is  1725. 

Explanation. — After  arranging  the  niimljers  as  in  ^  88,. 
we  are  required  to  take  6  units  from  1  unit:  this,  of  cou^rse,. 
we  can  not  do.  But  (§  87)  the  difference  between  two  num- 
bers is  not  changed  by  increasing  those  numbers  equally. 
So  we  add  10  units  to  the  1  unit  of  the  minuend,  making 
11  units,  from  which  we  subtract  the  6  units  of  the  subtra- 
hend, getting  5  units  for  the  remainder.  Then,  since  we 
increased  the  minuend  10  units,  we  must  indrease  the  sub-  . 
trahend  the  same  amount  :  aod  do  this  by  adding  1  ten 
(equal  to  10  units)  to  the  3  tens  of  the  subtrahend.  Hence 
we  say,-  ♦4  from  6  leaves  2."  In  the  column  of  hundreds 
we  meet  the  same  difficulty,  and  avoid  it  by  adrding  10  hun- 
dreds to  the  minuend,  and  afterwards  1  thousand  (equal  to 
10  hundreds)  to  the  subtrahend. 

Ex.  12.  From  123456  take  9876. 

123456  §90.     Model.— 6  from  6  leaves  0;   7 

9876         from  15  leaves  8  ;  9  from  14  leaves  5;  10 

113580         from  13  leav.es  3  ;    1  from   2   leaves  1 ;    0 

fr^m  1  leaves  1.     The  remainder  is  113580. 

We  may  now  give  the  following 

RuLy  FOR,  Subtraction. — Place   the  subtrahend   under 
the  minuend,  with  units  of  the  same  order  in  the  same  column. 

Beginning  at  the  right,  take  each  figure  of  the  subtrahend 
from  the  corresjyonding  figure  of  the  minuend. 

If  an?/  figure  of  the  minuend  is  less  than  the  correspond-^ 
ing  figure  of  the  subtrahend,  add  10  to  this  minuend  figure, 
and  add  1  to  the  suj^trahend  figure  in  the  next  column. 

PnooF. — -J.  Add  the  remainder  to  the  subtrahend  ;  the- 
sum  will  be  equal   to  the  minuend.  , 

65  E 


§y^ 


PRIMARY   ARITHMETIC. 


Or,  2.  Subtract  the  remainder  from   the  minuend  ;  the 
difference  will  be  equal  to  the  subtrahend. 


Ex.  13.  From  270  take  195. 

14.  From  381  take  18G. 

15.  From  492  take  275. 

16.  From  5104  take  386. 

17.  From  6215  take  497. 

18.  From  7326  take  5108. 
•    19.  From  8435  take  6229. 

20.  From  9326  take  6340. 

21.  The  minuend  is    10437  ; 
what  is  the  remainder  ? 

22.  The  minuend  is   21548 
what  is  the  remainder  ? 


Rem 
the   subtrahend    is 

Eem 
the   subtrahend    is 

Rl^i.  12861 


■  Rem.  75. 
Rem.  195. 
Rem.  217. 
Rem.  4718. 
Rem.  5718. 
Rem.  2218. 
Rem.  2206. 
2986. 
7465; 
2972. 
8887: 


23.  The  minuend  is   30435  ;    the    subtrahend    is   9798  ; 
what  is  the  remainder?  Rem.  20637. 

24.  The  minuend  is  49324 ;   the  subtrahend   is   10899  ; 
what  is  the  remainder  ?  Rem.  38425. 

25.  The  minuend  is  "58213;    the    subtrahend   is   21911; 
what  is  the  remainder?  Rem.  36302. 

26.  The  minuend  is  67102 ;    the    subtrahend    is   32823  ; 
what  is  the  remainder  1  ,  Rem.  34279. 

27.  The  minuend  is  78901 ;   the    subtrahend   is  41723 ; 
what  is  the  rema^inder  ?  Rem.  37178. 

28.  The  minuend  is  891012  ;   the  subtrahend  is  50612  ; 
what  is  the  remainder  ?  ,  Rem.  840400. 

29.  The  minuend  is  9102123  ;    the  subtrahend  is  61501 ; 
what  is  the  remainder?  Rem.  9040622. 

30.  The  minuend  is  10213435  ;  the  subtrahend  is  76522; 
what  is  the  remainder?  Rem.  10136913. 


31.  The  subt'd  is  10213435  ; 
what  is  the  remainder  1 


the  minuend  is  53431201  . 
Rem.  43217766'. 


66 


SUBTRACTION.  §90 


32.  The  subt'.d  is  21345647  ;  the  minuend  is  534312010  ; 
what  is  the  remainder?  Eem.  512966363. 

33.  The  subtrahend  is  21345;    the  minuend  is  312010: 
what  is  the  remainder  ?  *         "  '   Eem.  290665. 

34.  The  subtrahend  is  121345;    tlie  minuend  is  312010 ; 
what  is  the  remainder  ?  ^  Rem.  190665. 

35.  The  subt'd  is  6121345  ;    the  minuend  is  31201016; 
what  is  the  remainder  ?  Rem.  25079671. 

36.  The  subt'd  is  5431216;    the  minuend  is   31201016; 
what  is  the  remainder  ?  .  Rem.  25769800. 

37.  The  KubtM  is  6320105;   the  minuend  is  -42315427  ; 
what  is  the  remainder'/  Rem.  35995322. 

38.  The  subt'd  is  7210094;    the  minuend  is  53426739; 
what  is  the  remainder?  Rem.  46207645. 

39.  The  subt'd  is  8321125;    the  minuend  is  42115628; 
what  is  the  remainder  ?  Rem.  33994503. 

40.  The  subt'd  is  9432167  ;   the  minuend  is  31204517; 
what  is  the  remainder?  Rem.  21772350. 

41.  What  is  the  difference  between  24680  and  86042  2 

Ans.-  61362. 

42.  What  is  the  difference  between  25  and  25000  2 

Ans.  24975. 

43.  What  is  the  difference  between  9000000  and  9  ? 

Ans.  8999991. 

44.  What  is  the  difference  between  95000  and  950  ? 

Ans.  94050. 

45.  What  is  the  difference  between  13579  and  97531  ? 

Ans.  83952. 

46.  What  is  the  difference  between  24680  and  8642  ? 

Ans.  16038. 

47.  What  is  the  difference  between  35791  and  9753  ? 

Ans.  26038. 

48.  What  is  the  difference  between  1000000  and  1  ? 

Ans.  999999. 
67 


§90  PRIMARY    AUITIIMETIC. 


49.  What  is  the  difference  betwceu  200000  aud  200  ? 

Aius.  199800, 

50.  What  isjthe  difference  between  45000  and  45  ? 

Ans.  44955.  " 


PROMISCUOUS  PROBLEMS. 

1.  A  farmer  raised  on  one  field  425  bushels  of  corn,  or; 
an  other  379  bushels,  and  on  a  third  10'^  otishels ;  how  iiiany . 
bushels  did  he  raise  on  all  three  1  An>\  1002  bushels. 

2.  A  man  lent  2550  dollars  to  one  fneuu,  3775  dollais 
to  an  other,  and  kept  1575  dollars  for*  his  own  use;  how 
much  money  had  he  at  first  ?  Ans.  7900  dollars. 

3.  A  merchant  bought  a  case  of  silk  fur  3740  dollars,  and 
sold  it  for  3387  dollars;    how  much  did  he  lose  on  it  ? 

Ans.  353  dollars. 

4.  The  same  man  bought  a  quantity  of  linen  for  2465- 
dollars,  and  sold  it  at  a  profit  of  1233  dollars  ;  how  much 
did  he  receive  for  it  t  •   Ans.  3698  dollars.. 

5.  I  bought  525  barrels  of  flour,  and  sold  it  all  but  238 
barrels  ;  how  much  did  I  sell  ?  Ans.  287  barrels. 

6.  I  wish  to.  buy  a  tract  of  laud  for  5000  dollars,  and  I 
have  only  3775  dollars  on  ha'nd  ;  how  much  money  do  I 
lack  ?  Ans.  1225  dollars. 

7.  By  selling  a  farm  for  3000  dollars,  I  gain  875  dollars  j 
what  did  I  give  for  it?  "  Ans.  2125  dollars. 

8.  I  bought  3  bales  of  Stowe's  domestic,  containing  re- 
spectively 985 yards,  1063  yards, and  1187  yards;  how maoy 
yards  did  I  buy  in  all  ?  Ans.  3235  yards. 

9.'  I  bought  one  lot  of  coffee  for  786  dollars,  and  an  other 
for  695  dollars,  and  sold  one  lot  for  875   dollars,  and  the 
68 


SUBTRACTION.  §90 


other  for  200  dollars  less;  bow  much  did  I  gain  or  lo&e  in 
all  ?  Ans.  I  ^ined  69  dollars. 

10.  A  merchant  wont  to  market  with  10000  dollars,  and 
laid  out  2569  dollars  for  dry  goods,  2147  dollars  for  gro- 
ceries, 1728  dollars  for  hittdware,and  975  dollars  for  queens- 
ware  ;  4iow  ni'uch  money  did.  he  bring  home,  provided  bis 
trip  cost  him  81  dollars?  Ans.  2500  dollars. 

11.  A  merchant  made  a  collecting  tour :  in  one  town  he 
collected  1075  dollars;  in  an  other,  2128  dollars;  in  a 
third,  1357  dollars;  and  in  a  fourth,  809  dollars;  he  had 
50  dollars  with  him  when  he  started,  and  his  expenies  for 
the  whole  tour  were  105  dollars;  how  much  money  did  he 
bring  home  ?  •  Ans.  5374  dollars. 

12.  A  dealer  bought  25  bolts  of  cloth  containing  altogeth- 
er 700  yards  ;  aRer  selling  18  bolts  containing  578  yards, 
how  many  yards  had  he  left  ?  Ans.  122  yards. 

J.O.  .Four  men  contribute  to  the  founding  of  a  school  r  A 
gives  1000  dollars  ;  B,  245  dollars  more  than  A ;  C,  176 
dollars  less  than  B  ;  and  D,  233  dollars  more  than  C ;  how 
much  does  J)  contribute  ?  Ans.  1302  dollars. 

14.  A  farmer  raised  253  bushels  of  wheat,  which  is  149 
bushels  Ipss  than  he  raised  last  year  ;' how  much  did  he 
raise  last  year  ?  '     Ans.  402  bushels. 

15.  I  borrowed  1000  dollars  from  a  friend ;  since  then  I 
have  paid  him  at  different  times  225*  dollars,  239  dollars, 
and  397  dollars  ;  how  much  do  I  still  owe  him  ? 

,  Ans.  139  dollars. 

16.  A  man  who  had  2465  acres  of  land,  gave  one  of  his 
sons  729  acres^  and  an  other  oTS  acres ;  how  many  acres 
had  he  left  ?  Ans.  1163  acres. 

.17.  A  farmer  raised  876  bushels  of  wheat,  and  sold  147 
b  ishels,  and  had  208  bushels  ground  into  flour  ;  how  many 
buhbels  had  he  remaining.?  Ans.  521  bushel.^. 

69 


§91  PRIMARY   AaiTHMETIO. 


18.  If  the  mijijuend  is   300300,   and    the   remainder    is 
48729,  what  is  the  subtrahend?  Ans.  251571. 

19.  If  the  subtrahend  is  300300,  and    the    remainder   is 
48729,  what  is  the  minuend  ?  Ans.  349029. 

20.  If  the  subtrahend    h   0:/:784,    and    the    minuend   is 
300300,  what  is  the  remainder?  Ans.  207516. 

21.  If  the  subtrahend^is   568913,    and    the    minuend    is 
891356,  what  is  the  remainder  ?     ,  An;,.  322443. 

22.  If  the  subtrahend  is  123456789,  and  the  minuend  is 
987654321,  what  is  the  remainder  ?  Ans.  S64197532. 


MULTIPLICATION. 

§91.     Multiplication  is  the  operation  of  finding  a  Durn 
bef  which  shall  contain  one  of  two  given  numbers  as  mapy 
times  as  there  are  units  in  tJie  otue:-. 

§92.  The  numher  to  he  mulii'j/  '•  I  is  called  the  muUi- 
plicand. 

§  93.     The  multipli/ing  number  is  called  tlie  muItipUer. 

§  94.     The  result  of  multiplication  is  called  the  product. 

§  95.  Either  the  multiplicand  or  the  multrplier  is  called 
a  factor  of  the  product,  and  they  both  -ire  called  its  factor.<. 

§96.  An  ahsiract  ii\Vim.hQV  is  one  whose  unit  is  notsnec- 
ified  ;  as,  two,  forty,  seven,  twenty -seven. 

§97.  A  concrete  number  is  one  vfhose  unit  is  specified  ; 
as,  five  dollars,  ten  men,  sixteen  books. 

§  98.  The  product  of  any  tv^o  abstract  factors  is  the 
same,  no  matter  which  is  used  as  multiplier.  Thus,  3  times 
6,  and  6  times  3,  are  each  equal  to  18;  4  times  5  is  equal 
to  5  times  4. 

Before   proceeding   further,    let    tlic    pupil   thoroughly 

memorize  the  following  Table. 
70 


MULTIPLICATION. 


§98 


]MU1L.TI1?'L.ICA.T10]?^     TJk]BL.3i]. 


Once 

0 

is 

0 

Twice 

0 

are 

0 

o 
•J 

times 

0 

are 

0 

Once 

1 

n 

1 

Twice 

1 

are 

2 

n 

timei' 

1 

arc 

3 

Once 

2 

IS 

2 

Twice 

2 

are 

4 

3 

times 

2 

are 

() 

.  Once 

3 

is 

3 

Twice 

3 

fvre 

6 

3 

times 

3 

are 

9 

Odco 

4 

IS 

4 

Twice 

4 

are 

8 

3 

times 

4 

are 

12 

Once 

5 

IS 

5 

Twice 

5 

are 

10 

3 

times 

5 

are 

15 

Once 

G 

IS 

6 

Twice 

6 

are 

13 

3 

times 

6 

are 

18- 

Onoc 

7 

IS 

7 

Twice 

< 

are 

14 

3 

times 

7 

are 

'21 

Once 

8 

is 

8 

Twice 

8 

are 

IG 

S 

times 

8 

are 

24 

Once 

9 

is 

9 

Twice 

9 

are 

18 

3 

times 

9 

are 

27 

Once 

W 

is 

10 

Twice 

10 

are 

2U 

3 

times 

10 

are 

30 

Once 

11 

is 

11 

Twice 

n 

arc 

22 

3 

times 

11 

are 

33 

One  3 

12 

is 

12 

Twice 

12 

are 

24 

3 

times 

12 

are 

36 

4 

times 

0 

are 

are 

0 

5 

times 

0 

are 

0 

'  G 

times 

0 

aro 

0 

4 

times 

1 

4 

6 

times 

1 

are 

6 

G 

times 

1 

are* 

G 

4 

times 

>) 

are 

8 

5 

times 

2 

are 

10 

G 

times 

•t 

are 

12 

.■> 

•4 

times 

3 

are 

12 

5 

times 

3 

are 

15 

6 

times 

3 

are 

IS 

4 

.times 

4 

are 

16 

5 

times 

4 

are 

20 

G 

tiroes 

4 

are 

24 

4 

times 

5 

are 

20 

5 

times 

5 

are 

25 

6 

times 

5 

are 

30 

4 

times 

6 

are 

24 

5 

times 

5 

are 

30 

6 

times 

G 

are 

3G 

4 

times 

7 

are 

28 

5 

times 

7 

are 

35 

6 

times 

7 

arc 

42 

4 

times 

8 

are 

^2 

5 

times 

8 

are 

40 

€ 

times 

8 

are 

48 

4 

times 

9 

are 

3^ 

5 

times 

9 

aro 

45 

G 

times 

9 

aro 

54 

4. 

times 

10 

are 

40 

5 

times 

10 

are 

50 

6 

timea 

10 

are 

60 

4 

times 

11 

are 

44 

6 

times 

11 

are 

55 

G 

times 

11 

are 

GG 

4 

times 

12 

are 

48 

5 

times 

12 

are 

GO 

G 

timws 

12 

are 

72 

7 

limes 

0 

nrc 

0 

8 

times 

0 

are 

0 

9 

times 

0 

are 

0 

7 

times 

1 

are 

8 

times 

1 

are 

8 

9 

times 

1 

are 

9 

7 

times 

n 

are 

14 

8 

times 

2 

j^re 

IG 

9 

times 

o 

are 

18 

7 

times 

3 

are 

21 

8 

times 

3 

are 

24 

9 

times 

s 

are 

27 

7 

times 

4 

are 

28 

8 

times 

4 

are 

32 

9 

times 

4 

are 

3C 

7 

times 

5 

are 

55 

8 

times 

5 

are 

40' 

9 

times 

5 

are 

45 

7 

times 

6 

are 

42 

8 

times 

G 

are 

48 

9 

times 

6 

aro 

54 

7 

times 

7 

are 

49 

8 

times 

7 

are 

56 

9 

times 

7 

are 

63 

7 

times 

8 

are 

5G 

8 

times 

8 

arc 

G4 

9 

times 

8 

are 

72 

7 

times 

9 

are 

OS 

8 

times 

9 

are 

72 

9 

times 

9 

are 

81 

7 

times 

10 

are 

70 

8 

times 

10 

are 

80 

9 

times 

10 

are 

90 

7 

times 

11 

are 

77 

8 

tiroes 

11 

aro 

S8 

9 

times 

11 

are 

99 

7- 

times 

12 

are 

84 

8 

times 

12 

are 

96 

9 

times 

12 

are 

1G8 

71 


;99 


PRIMARY   ARITHMETIC. 


10  times 
10  times 
10  times 
10  times 
10  times 
10  times 
10  times 
10  times 
10  limes 
lOJtimes 
10  times 
10  times 
10  times 


0  are 

1  arc 

2  are 

3  are 

4  are 

5  are 

6  are 

7  are 
S  are, 
9  are 

10  are 

11  are 

12  are 


0 

11  times 

0 

are 

0 

12  times 

0 

are 

(J 

10 

11  times 

1 

arc 

n 

12  times 

1 

are 

12 

20 

11  times 

r* 

are 

22 

12  time.? 

2 

are 

24 

30 

11  times 

3 

are 

33 

12  times 

3 

are 

36 

40 

11  times 

4 

are 

44 

12  times 

4 

are 

48 

50 

11  time3 

5 

are 

55 

12  times 

5 

are 

60 

60 

11  times 

6 

are 

66. 

12  times 

6 

are 

72 

70 

11  times 

7 

are 

,   77 

12  times 

7 

are 

84 

80 

11  times 

8 

are 

88 

12  times 

8 

are 

96 

90 

11  times 

9 

are 

99 

12  time^ 

9 

are 

103 

100 

11  times 

10 

are 

no 

\l  times 

10 

are. 

120 

110 

11  times 

11 

are 

121 

12  times 

Ji 

are 

132 

12(7 

11  timed 

12 

are 

132 

12  times 

12 

are 

144 

1^99.  The  multiplier  must  al^vays  be  an  abstract  num- 
ber, and  the  product  is  always  like  the  multiplicand.  Thus, 
to  find  the  cost  of  5  yards  of  cloth  at  10  cents  a  yard,  it  is 
evident  that  we  can  not  multiply  10  cents  by  5yards;  that 
is,  we  can  not  say,  5  yards  times  10  cents  :  but  we  multiply 
10  cents  by  5,  and  this  evidently  gives  50  cents. 

Ex.  1.  Multiply  2423  by  2. 


2423 

2 

4846 


SIOO.  Model.— Twice  3  are  6;  twice  2 
are  4  ;  twice  4  nrc  8  ;  twice  2  are  4?  The 
product  is  4846. 

Explanation, — The  smaller  factor  is  placed  under  the 
larger.  Then,  beginning  af  the  right,  each  figure  of  the 
upper  number  is  taken  twice,  and  each  product  is  set  under 
the  figure  which  produced  iit.  For,  since  the  product  is 
always  like  the  multiplicand,  (§99,)^  twice  3  units  are  6 
units,  twice  2  tens  are  4  tens,  &c,  .  '      . 

Ex.  2.  Multiply  1203  by  2, 

3.  Multiply  130420  by  2. 

4.  Multiply  20301402  by  2. 

5.  Multiply  2030102  by  3. 

6.  Multiply  1203201  by  'i. 

72     ^ 


Prod.  2406. 

Prod.  260840. 

Prod.  40602804. 

Prod.  6090306. 

Prod.  3609603. 


"^lU  LTJ  PL  r  CATION.  §10! 


7.  Multiply  2310132  by  3.  Prod.  6980396. 

8.  Multiply  21012  by  4.  Prod.  84048. 

9.  Multiply  102120  by  4.             -    ^  Prod.  408480. 

10.  Multiply  lOUOl  by  5.  Prod.  505505. 

11.  Multiply  12345  by  4. 

12345  §101.    MoDKL. — 1  time?  5  fire  20;  4  times 

4         4  are  16,  and  2  are  18;  4  times  3   are   12, 

49380         ^^^  ^  ^^^  ^^  '  "^  ^^^'^^^''^  '^  ^^'^'  '^'  ""^^  l_are9  ; 
4  times  1  arc  4.     The  product  is  49380. 

,  Explanation.— When  we  multiply  5  unit.?,  by  4,  we  get 
'^:0  units;  and,  since  this  is  expressed  by  two  figures,  it  caii 
not  be  written  in  the  place  of  units  :  lience,  as»in  addition, 
^  81,  we  set  down  the  0  in  the  place  of  units,  and  reserve 
the  2  to  be  added  to  the  16  tens,  which  we  get  by  multiply-  . 
ing  4  tens  by  4.  Again,  sinec  18  tens  are  equal  to  1  hun- 
dred and  8  tenF,we  .set^8in  the  place  of  ten^■,  and  reserve 
the  1  hundred  to  be  added  to  the  product  of  3  hundreds 
by  4.        - 

Ex.  12.  Multiply  53706  by  3.  Prod.  158118. 

13.  Multiply  27.95  by  2.         ^  Prod.  5590. 

14.  Multiply  1684  by  3.  Prod.  505?. 

15.  Multiply  3810G  by.5.'    *  Prod.  190530. 

16.  Multiply  49217  by*6.  Prod.  295302. 

17.  Multiply  510328  by  7.  Prod.  3572296. 
.18.  Multiply  621439  by  8.  Prod.  4970712. 
19.  Multiply  7325410  by  9.  Prod.  65928690. 
29.  Multipfy  8436521  by  10. 

o^ot'AoiA  §102.  MoDLiL. — Annex  one  naught  to  the 

84365210       j^uuipiicaiid.     The  product  is  84365210. 

Explanation.— Since'lO  units  of  any  order  make  one  of 

the  next  order  on  the  left,  any  number  is  multiplied  by  10 

by  merely  moving  eiich  of  its  figures  ont3  place  to  the  left, 

and  puttin.^  a  0  in  the  place  of  units.     So,  if  the  multiplier 

73 


1 103  prima;?y  abithmetic. 


is  cojiiposed  of  1  with  naugbts  annexedj  the  produofc  is  ob- 
tained by  simply  aiinesing   to  the   multiplicand  as   many 
naughts  an  there  are  a6  the  right  of  the  1  in  the  multiplier. 
Ex.  21.  Multiply  31597  by  10.  Prod.  315970. 

22.  Multiply  426108  by  100.  Prod.  42610800. 

23.  Multiply  537219  by  10.  Prod.  5372190. 

24.  Multiply  6483210  by  100.  Prod.  648321000. 
*25.  -^lultiply  759432Kby  1000.            Prod.  7594321000. 

26.  Multiply  12345  by  50. 

§  103.     MoDiiL. — 5  times  5  are  25 ;   5 

12345  times  4  a^e  20,  and  2  are  22;    5  times  3 

50         are  15,  and  2  are  17  ;  5  times  2  are  10,  and 

617250         1  are  11 ;  &  times  1  are  5,  and  1  are  6  : — 

annex  0.     The  product  is  617250. 

Explanation. — We  first  multiply  by  5,  as  in  §101; 
and  ihen,  since  50  is  10  times  5,  we  multiply  thi«  product 
by  10,  as  in  §  102,  to  get  the  true  product. 

Ex.  27.  Multiply  6172  by  20.  Prod.  123440. 

28.  Multiply  7283  by  30.  Prod.  218490. 

29.  Blultiply  8391  by  40.  Prod.  335760. 

30.  Multiply  94105  by  500.  Prod.  47052500. 

31.  Multiply  105216  by  60.  Prod.  6312960. 

32.  Multiply  216327  by  700.  Prod."  151428900. 

33.  Multiply  317438  by  80.  Prod.  25895040. 
H.  Multiply  428549  by  900.                  Prod.  385694100. 

25.  Multiply  246  by  35. 

§  104.     Model. — 5  times  6  are  30  ;  5  Iflmes 

246         4  are  20,  and  3  are  23  ;  5  times  2  are  10,  ana 

35         2  are  12* — 3  times  6  are  18,  set  down  B  un- 

1^0         der  3 ;  3  times. 4   are   12,  and   1   are   13;  3 

ygg  times  2  are  6,  and  1  are  7: — add  the  partial 

—j —         products:  0;  8,  and  3  are  11 ;  land  3  are  4, 

^^^^         and  2  are  6  ;    7  and  1  are  8.     The  product  is 

86J0. 

74 


"multiplication.  1^104 


Explanation. — The  upper  number  is  inultiplied,  first 
by  5.  as  in  §*101,  and  then  by  -^0,  aa  in  §  103,  except  tb.t 
the  0  at  the  right  is  omitted,  as  being  unnecessary,  .^ince 
the  ee\*feral  figures  can  bo  placed  iu  their  proper  columns 
without  it.  It  must  hf^  remembered,  however,  that  the 
second  partial  product  is  not  738,  but  7380. 

We  may  now  give  the  following 

RULK  FX>R  MuLTIPrJCATION. — 1.  When  either  factor 
contains  hut  one  valual>Jc  Jigure.  Set  the  smaller  factor  un- 
der the  larger.  Beginning  at  the  right,  multiply  each  figure 
of  the  upper  nvmher  hy  the  lower  number,  set  down,  the  right 
hand '^gure  of  the  product,  and  add  the  remaining  figure, 
if  any,  to  the  next  'product  ;  hut  set  down  the  tvhole  of  the 
last  2>i'odiict. 

2.    When  tlie  smaller  factor  <ontains  more  th(!n  one  volua 
hie  figure. _    Set  it  under  the  larger  ;  m,ultiph/  the  tipper  fac- 
t-yr  hy   each  figure  of  the   lower.  Betting   the  first  figure  of 
each  partial  product  under  the  multiplying  figuje  irhich  pro- 
duced it^  S'nd  add  the  partial  products  together  in  tha.{  order. 

Proof. — Multiply  the  lower  factor  by  the  upper. 

Ex.  36.  Multiply  357  by  46.    ,  Prod.  16422. 

37.  Multiply  468  by  57.  ^         '  Prod.  2G676. 

38.  Multiply  579  by  68.  *  -  Prod.  39372. 

39.  Multiply  G810  by  70.  Prod.  537990. 

40.  Multiply  7021  by  810.  Prod.  6416010. 

41.  Multiply  8132  by  92.  Prol  74814-1. 

42.  Multiply  0243 .by  103.  •  Prod.  95201:9. 

43.  Multiply  10354  by  214.  Prod.  2215756. 

44.  iMuItiply  21456  1>Y  325.  Prod.  6973200. 

45.  Multiply  32567  by  430.  Prod.  14190212. 

46.  Multiply  43G78  hy  547.  Prod.  23891866. 

47.  Multiply  54789  by  C58.  Prod.  30551162. 


<o 


§104 


PRIMARY  •.vBIinME'DlC. 


49- 
50. 
51. 
52! 

53. 

,"-  t 

•  >-r. 

55. 
56. 
57. 
58. 
59. 
60. 
61. 
62. 
63. 
64. 
65. 
Q6. 
67. 
68. 
69. 

70. 

>- « 
/  i. 

72. 

73. 

74. 

75. 

76. 

77. 

78. 

79. 


Multiply  658 109  by  769. 
Multiply  7692110  by  8710. 
Multiply  87103251  by  9'821. 
Multiply  98214  by  10932.. 
Multiply  109325"by  21104. 
Multiply  2110436  by  31254. 
Multiply  321547  by  42365. 
Multiply  342658  by  53476. 
Multiply  453769  by  64S7. 
Multiply  564760 'by  7598. 
Multiply  675671  by  86109. 
Multiply  786952  by  97210. 
Multiply  897063  bv  10832. 
Multiply  908174  by  20943. 
Multiply  108:195  by  31.054. 
Multiply  2092105  hj  42165. 
Multiply  31103216  by  5827. 
Multiply  42214327  by  6138. 
Multiply  1203450  by*9004. 
Multiply  9087061  by  56708. 
Multiply  8706544  by  67089. 
Multiply  4321209  by  12340j, 
Multiply  3456789  1^-  5G7C90. 
xMultiply  598750  ii)^  32451. 
Multiply'5007631  by  43976. 
Multiply  423455  bj  3250. 
Multiply  536527  by  1864. 
Multiply  25876  by  2864. 
Multiply  47237  by  3526. 
Multiply  95423  by  8721. 
Multiply  58792  by  4587. 
Multiply  67813  by  l-.'525. 
Multiply  243685  by  4372. 
76  -*^ 


Prod.  506085821. 

Prod.  G7075199200. 

Prod.  855441028071. 

Prod.  1073G>5448. 

Prod.  2307194800. 

P^od.  65959566744. 

Prod.  13623338655. 

Prod.  18323979208. 

Prod.  2913599503. 

Prod.  4291046480. 

Prod.  58181354139. 

Prod.  76499603920. 

Prod.  971G983416. 

Prod.  19019891082. 

Prod.  3362992930. 

Prod.  8y213o0V325. 

Prod.  165686831632. 

Prod.  271775837226. 

Prod.  40835863800. 

Prod.  5153>90551S8. 

Prod.  584113330416. 

Prod.  533276081481. 

Prod.  1960310474010. 

Prod.  19430036250. 

Prod.  220215580856. 

Prod.  1377499115. 

Prod.  100C086328. 

Prod.  74108864. 

Prod.  166557662. 

Prod.  832183983. 

Prod.  260G78904. 

Prod.  849357825. 

Prod.  1 065390820. 


DIVlSluW.  §110 

81.  Mulriplj  89554S  by  1028'G.  Prod.  406800072^'. 

8h  Maltipiy  ('65528  by  8765.  Prod.  58333521)20. 

8:1  Multip]}'^  278963  by  7782.  Prod.  2170890060. 

84.  Multiply  142986  by  0-17.  Prod.  1317441112. 

85.  Multiply  111375  by  2242.  Prod.  249702751). 
8C.  Multiply  9.;97G3  by  8765.  Prod.  8762022695. 
87.  Multiply  87G543  by  5462.  .  Prod.  4787G77860. 
$8.  Multiply  275684  by  4827.  Prod.  13307266GS. 


DIVISION. 

§105.  Division  is  the  operation  of  finding  how  mciny 
times  one  number  is  cont:iined  in  an  other.     Or, 

§  106.  Division  is  the  operation  of  separating  a  number 
into  some  number  of  equal  part?. 

Thus,  if  I  spend  15  cents  for  lace  at  5  cents  a  yard,  the 
work  consists  in  finding  how  many  times  5  cents  is  con- 
tained in  15  cents,  and  this  number  of  times  is  equal  to  the 
number  of  yards  I  get. 

But,  if  I  pay  15  cents  for  3  yards  of  lace,  the  work  con- 
sists in  separating  15  cents  into  3  equal  pilrts,  and  each  one 
of  these  parts  is  the  price  of  a  yard. 

§  107.     The  number  to  he  divided  is  called  the  diifidcnd. 

§  108.     The  dividivj  number  is  called  the  Jivisar. 

§  109.    'The  result  of  division  is  called  the  quotient. 

§110.  When  the  division  is  not  complete,  the  undi- 
vided part  of  the  dividend  is  called  the  remainder. 

Thus,  9  in  29,  3  times,  with  2  over  :  here  29  is  the  divi- 
dend, 9  is  the  divisor,  3  is  tho  quotient,  and  2  is  the  re- 
mainder. 

Before  proceeding  further,  let  the  pupil  tlioroughly 
memorize  the  following  Table.  • 

77 


§110 


PRIMARY   ARITHMETIC. 


I31VXfe!5IOINr    'X^JVBLJE. 


]    ir. 

0, 

no  time 

2 

in 

0, 

no  time 

3  in     0,  no  time 

1   in 

1, 

o'ace 

2 

in 

') 

once 

3  in     3,  once 

i   iii 

"1 

twice 

o 

in 

4,' 

twice 

3  in     6,  tv;ice 

1  ill 

3, 

3  times 

2 

in 

0, 

3  times 

3  in     9,   3    times 

1  in 

4, 

4  times 

o 

ill 

8, 

>  4  times 

3  in  12,  4   times 

1   iu 

5, 

5  times 

2 

in 

10, 

5  times 

3  in  15,  5   times 

1  in 

6, 

G  times 

2 

in 

y-^, 

G  time^ 

3  in  18,  0    times 

i   in 

7 

7  times 

2 

in 

14, 

7  titpe-^ 

3  in  21,  7    times 

1  in 

8. 

8  times 

2 

in 

^^ 

8  times 

3  in  24,  8    times 

1  in 

0, 

ii  times 

in 

18, 

9  times 

3  iu  27,  9    timec 

4  in 

0, 

no  timo,        i 

5 

in 

0. 

no*  time        ! 

G  in     0,   no  lime 

4  in 

4, 

onc;:i 

5 

in 

'^ 

0!ice              1 

'6  in     G,  once 

4  in 

B, 

twice            1 

*  5 

iu 

10, 

twice 

G  in  12,  twice 

4  iu 

12, 

3  times        ! 

h 

ia 

15, 

3  times        I 

G  in   18    3    times 

•1  in 

Ifi, 

4  times. 

5 

in 

20, 

4  times        j 

G  in  24,  4     times 

4   ia 

20, 

5  times 

5 

\n 

25, 

5  times        ' 

6  iu  30,   5    times 

4  in 

24, 

0  times 

5 

in 

30, 

6  times 

6  in  36,   G    times 

4  ill 

28, 

7  times* 

5 

in 

35, 

7  times 

6  in  42,    7     times 

4  in 

32, 

8  times 

T; 

in 

40, 

8  "limes 

6  in  48,   8    times 

4  in 

36. 

9  timed 

5 

iu 

45, 

9  times    . 

6  in  54,  0    times 

7  ia 

0, 

no  time 

8 

in 

0, 

no  time 

9  in     0,  no  time 

7  in 

7, 

once 

8 

in 

8. 

once 

9  in     9,  unce 

7  in 

14, 

twice 

8 

in 

16, 

twice 

9  in  18,  twice 

7  in 

21, 

3  timec 

8 

in 

24, 

3  times 

9  in  27,  3    timei 

7  in 

28, 

4  limes 

8 

in 

32, 

4  times 

9  in  36,  4    times 

7  in 

35, 

5  time§' 

1       8 

in 

40, 

5  times 

9  in  4^\-  5    times 

7  in 

42, 

6  times 

8 

In 

48, 

C  times 

9  in  54,  6    times 

7  in 

49, 

7  times 

8 

in 

56, 

7  times 

9  in  63,  7    times 

7  in* 

56, 

8  times 

8 

in 

64, 

8  times  ' 

9  in  72,  8    times 

7  in 

dp, 

9  times 

8 

in 

72, 

9  times 

9  in  81,  9   times 

10  in 

0, 

no  time 

11 

in 

0, 

no  time 

12  in       0,  no  time 

10  in 

10, 

once 

11 

in 

11, 

once 

12  in     12,  once 

1.0  in 

20, 

twice 

11 

in 

22, 

twice 

12  in     24,  twice 

10  in 

30, 

3  times 

11 

in 

oo. 

3  times 

12  in     36,  3  times 

10  in 

40, 

4  times 

11 

in 

44, 

4  times 

12  in     48,  4  times 

10  in 

50, 

5  times 

•11 

in 

55, 

5  times 

12  in     60,  5  times 

10  in 

60, 

G  times 

1     11 

in 

66, 

6  times 

12  in     72,  6  times 

10  in 

70, 

7  times 

M 

in 

77, 

7  times 

12  in     84,  7  times 

10  in 

80, 

8  times 

11 

in 

88, 

8  times 

12  in     96,  8  times 

10  in 

90 

9  trim6s 

11 

in 

99, 

9  tioles 

Vi  in  108,  9  times 

78 


DIVISION.  §112 


SHORT  DIVISION. 
Ex.  1.  Divide  24608  by  2. 


2V24608  '^  ^^^'    ^^^^'^^^''- — -^  ^"  ^-  <Jf''^'-' ;  --  i"  -^? 

*^— -^-— —  twice  ;  2  in  G,  3  times  ;    2  in  0,  no.  time  ; 

12304         2  in  8,  4  times?     The  qnoTicnt.  i«   '12804; 

Explanation. — The  divisor,  2,  is  placed  on  the  left  of 
the  dividend.  Then,  beginning  for  convenience  at  the  left, 
the  number  in  each  order  of  units  is  divided  by  2^  and 
each  (luotient  figure  is  set  under  the  one  from  vMiich  it  was 
obtained. 

Ex.  2.  Divide  3G090  by  3.  Quof.  12030. 

3.  Divide  28800  by  2.  Quot.  13400. 

4.  Divide  900  by  3.  Quot.  302. 

5.  Divide  8404  by  4.  ^  ^    •  Quot.  2101. 

6.  Divide  4808  by  4.      •  "  ^  Quot.*l202. 

7.  Divide  5055  by  5.  *  Quot.  1011. 
,    8.  Divide  660  by  6.  Quot.  110. 

9,  Divide  77  by  7.  Quot.  IJ. 

10.  Divide  808  by  8.  Quot.  101. 

11.  Divide  8565  by  5. 

-  <inRP.  '         §      "^*    Model. — 5  m  8,  once,  with  3 
^>l____         over;  5  in  35,  7  times;  5  in  6,  once,  with 
1713         1  over;  5  in  15,  3  times.     The  quotient  is 
1713. 
Explanation. — 5  is  contained  once  in  5  ;  so  that  there 
are  3   thousands  still  undivided.     Now,  3   thousands  are 
equal  to  30  hundreds,  and  this  added  to  the  5  hundreds  of 
the  dividend  gives  35  hundreds,  in  which  the  divisor,  5,  is 
contained  exactly  7  (hundred)  ti^es.     Again,  after  getting 
the  1  ten  of  the  quotient,  we  have  1  ten   of  the    dividend 
undivided.     This  is  equal  to  10  units,  which  added  to   the 
5  units  of  the  dividend,  makes  15  units,  in  which  the   divi- 
sor is  contained  exactly  3  times. 
79 


§llo 


I RI M.4 RY    AlUTilMe r I C . 


Ex.  n.  Divide  578  by  6. 

§  118.     Model. — G  in  57,  9  timet?,  with 
,     6j57o  3  over;  G  in  33,  5  times,  with  3  over,  set 

i^  3  down  5  ill  the  quotient,  and  3  as  remain- 
der. The  quotient  is  95,  and  the  remain- 
der 3. 

We  may  now  give  the  following* 

RuLS  FOR  Short  Divisiox. — Set  the  divuor  on  the  left 
of  the  dividend,  with  a  line  between  them,  and  one  under  the 
dividend. 

Beginning  at  thv,  left,  see  hoio  many  times  the  divisor  is 
contained  in  each  figure  of  the  dividend,  and  sat  the  result 
under  the  dividend. 

V/heneoer  there  is  a  remainder ,  prefix  it  to  the  next  fig- 
ure of  the  dividend,  before,  dividing. 

If  the  divisor  is  not  contained  en  any  figure^  cxcfjpt  the 
.first,  set  0  under  such  figure,  and  regard  it  as  a  remaiTider, 

Proof. — Multiply  the  q^iotient  by  the  divisor:  the  prod- 
uct, increased  by  the  remainder,  if  any,  will  be  equal  to 
the  dividend. 


Ex.  13.  Divide^684  by  2. 

14.  Divide  795  by  3.       . 

15.  Divide  8016  by  4. 

16.  Divide  9127  by  5. 

17.  Divide  10238  by  6. 

18.  Divide  21349  by  7. 

19.  Divide  324510  by  8. 

20.  .Divide  435621  by  9. 
21^  Divide  546732  by  10. 

22.  Divide  657848  by  11*. 

23.  Divide  768954  by  12. 

24.  "Divide  8791065  by  11. 

25.  Divide  98102176  by  10.' 

80    '  - 


Quot.  342. 

«      Quot.  265. 

Quot.  2004. 

.Quot.  1825,  Rem.  2. 

Quot.  1706,  Rem.  2. 

-     Quot!  3049,  Rem.  6. 

Quot.  40563,  Rem.  6. 

Quot.  48402,  Rem.  3.' 

Quot.  54673,  Rem.  2. 

Quot.  59803,  Rem.  10. 

Quot.  64079',  Rem.  6. 

Quot.  799187,  Rem.  8.. 

Quot.  9810217,  Rem.,6. 


DIVISION.  §114 


♦ 


26.  Divide  109213287  by  9.    Quot.  1^134809,  Rem.  6. 

27.  Divide  2110324398  by  8.   Quot.  263790549,  Rem.  6. 

28.  Divide  32214354109  by  7.  Quot.  46020505872,  Rem.  5. 

29.  Divide  433254652110  by  6.      Quot.  72209108685. 

30.  Divide  5443657632215  by  5.   Quot.  1088731526443. 

31.  Divide  6594768743324  by  4.   Quot.  1638692185831. 
32.,  Divide  766587985443  by  3.     Quot.  255529328481 
«83.  Divide  118456974  by  9.  Quot.  13161886.' 
34.  Divide  4546328  by  8.  Quot.  568291- 


-♦©♦- 


LONG  DIVISION. 

Ex   33.  Divide  7527  by  92. 

§114.     Model.— 9  in  75,  8  times ;  mul- 

7527192         tiply  the  divisor  by  8;  8  times  2  are  16  ; 

736   |g|         8  times  9  are  72,  and  1  are  73  :    subtract 

[^y  the  product  from  the  dividend ;  7 ;  6  from 

92  12  leaves  6  ;  4  from  -5  leaves  1 : — 9  in  16, 

— ^  once  ;    multiply  the  divisor  by  1 ;    once  2 

is  2 ;  once  9  is  9  :  subtract  the   product 

from  the  previous   remainder ;  2  from  7 

icavv^H  0  ;  9  from  16  leaves  7.     The  quotient  is  81,  and  the. 

remainder  75. 

Explanation. — The  divisor  is- now  placed  on  the  right 
of  i  i!    dividend,  for  convenience  in  multiplying.     The  num- 
ber 9  I-  used  as  a  trial  divisor.     As  one  figure  of  the  real 
':       '    )S  thus  omitted,  one  figure  of  each  partial  dividend 
.c  imiicted  also.     Hence,  since  we  use  75  as  a   trial 
'd,  the  real  first  partial  dividend  is  752,  and  we  set 
tir.st  figure  of  the  product  under  2,  one  place  to  the 
riviii     V  5.     The  8  of  the  quotient  stands  for  80  ;  and  hence 
the  fir  t  product  is  really  7360,  and  must  be  so  regarded  in 
snbtrtioiing. 


§115  PRIMARY  ARITHMETIC^ 


Ex.  34.  Divide  8932  by"29. 

§  115.     Model. — 3  io  8,  3  times  ;  mul- 
8932|29_       tiply  the  divisor  by  3  ;  3- times  9  are  27, 

87 |3()g       3  times  2  are  6,  and  2  are  8  :  subtract  the 

232  product  from  the  dividend  ;  3 ;  7  from  9 

232  leaves  2  : — 3  in  2,  no  time ; .  annex  2  : — 3 

t:  in  23,  8  times ;  multiply  the  divisor  by  8 ; 

8  times  9  are  72  ;  8  times  2  are  16,  and  7 
are  23  :  subtract   the   product   from  the 
previous  Remainder  ;  0.     The  quotient  is  308. 

Explanation. — If  the  second  figure  of  the  divisor  is  less 
than  5,  the  first  figure  is  the  trial  divisor ,  but,  if  the  sec- 
ond figure  is  greater  than  5,  the  trial  divisor  is  one  more 
than  the  first  figure.  This  trial  divisor  will  almost  always 
give  within  1  of  the  proper  quotient  figure,. and  will  usu- 
ally give  it  exactly.  If,  at  any  time,  however,  after  multi- 
plying, a  quotient  figure  is  found  to  be  too  small,  let  it  be 
increased  a  unit  at  a  timq^  until  the  correct  figure  is  found  ; 
and,  if  it  is  found  to  be  too  large,  let  it  be  diminished  in 
the  same  way. 

In  this  example,  the  first  product  is  really  8700  ;   but, 

after  we  begin  dividing,  every  remaining  figure  of  the  divi* 

,  dend  must  give  a  figure  of  the  quotient.     In  subtracting, 

therefore,  we  do  not  begin  *at  the  extreme  right,  as  we  usu- 

'    ally  do  ;  but  we  begin  only  one  figure  to  the  right  of  the 

first  partial  dividend. 

We  may  now  give  the  following 
'  Rule  for  Long  Diyision. -^JSet  the  divisor  on  the  right 
of  the  dividend,  with  a  line  between  them,  and  one  under  the 
divisor. 

Beginning  at  the  left,  see  how  often  the  divisor  is  contained 

in  the  first  part  of  the  dividend :  the  result  will  he  the  first 

figure  of  the  quotient.     Multiply  the  divisor  hy  this  quotient 

figure^  and  subtract  the  product  from  that  part  of  the  divi- 

•  82 


DIVISION.  §115 


dend  which  was  used,  annexing  to  the  remainder  the  next 
Jlgure  of  the  dividend. 

Take  this  remainder  as  a  second  partial  dividend,  and 
from  it  obtain  the  second  quotient  figure.  Multiply  the  divi- 
sor hy  this  figure,  and  subtract  the  product  from  the  previous 
remainder,  annexing  to  the  second  remainder  the  next  figure 
of  the  dividend. 

Continue  this  process  till  all  the  Jigures  of  the  dividend 
have  been  used. 

If  any  partial  dividend  will  not  contain  the  divisor,  set  0 
in  the  quotient,  annex  an  other  figtire  of^the  dividend,  and 
divide  again. 

^    Proof.  1.— The  same  as  in  §  113,  for  short  division. 

01-52.  Subtract  the  remainder,  if  any,  from -the  divi- 
dend ;  divide  this  remainder  bj  the  quotient,  and  the  re- 
sult will  be  the  divisor. 

Ex.  35.  Divide  672  by  21.  Quot.  32. 

36.  Divide  551  by  29.  Quot.  19. 

37.  Divide  864  by  32.  Quot.  27. 
•  38.  Divide  1444  by  38.  Quot.  38* 

39.  Divide  1008  by  42.  Quot  24.' 

40.  Divide  3478  by  47.  Quot.  74. 

41.  Divide  2091  by  51.  Quot  41 

42.  Divide  49358  by  58.  Quot.  *85l' 
,  43.  Divide  26596  by  61.  Quot.  436. 

44.  Divide  27068  by  67.  Quot.  404. 

45.  Divide  33361  by  73.  Quot.  457 

46.  Divide  36506  by  78.  *  Quot.  468. 

47.  Divide  23534  by  82.  Quot.  287. 

48.  Divide  43521  by  89.  Quot.  489 

49.  Divide  98901  by  99.  Quot!  99»! 

50.  Divide  98209  by  109.  Quot.  901. 

51.  Divide  112924  by  218.  Quot!  518 

83     • 


5115  PRIMARY   ARITHMETIC. 

52.  Divide  199143  by  327.  Quot.  609. 

53.  Divide  232824  by  436.  Quot.  534. 

54.  Divide  5815550  by  598.  Quot.  9725 


PROMISCUOUS  PEOBLEMS. 

1.  If  a  field  of  56  acres  produce  1232  bushels  of  vzneat, 
how  many  bushels  does  each  acre  produce  ? 

«  _  Ans.  22  bushels. 

2.  How  many  gallons  will  205  bai;<ls  contain,  if  each 
barrel  holds  27  gallons  ?   .  Ans.  5535  gallons. 

3.  Having  a  journey  of  900  miles  to  make,  I   have  al-  * 
ready  accomplished  279  miles  of  it ;  how  much  farther  have 

I  to  go  ?  Ans.  621  miles. 

4.  K  broker  loaned  275  dollars  to  one  man,  325  to  an 
other,  and  463  to  a  third  ;  how  much  do  the  three  together 
owe  him  ?  Ans.  1063  dollars. 

5.  A  merchant  bought  2575  dollars'  worth  of  dry -goods; 
and,  after  selling  to  the  value  of  2129  dollar,?,  he  has  on 
hand  916  dollars'  worth  ;  how  much  is  his  gain  on  the 
whole  ?  Ans.  470  dollars. 

6.  A  man  sold  a  tract  of  land  for  3000  dollars,  and  with 
the  proceeds  bought  45  head  of  cattle  at  45  dollars  a  head ; 
how  much  money  had  he  left  ?  Ans.  975  dollars. 

7.  A  maia  bought  8  yards  of  cloth  at  9  dollars  a  yard,  a 
silk  hat  for  5  dollars,  a  satin  vest  pattern  for  7  dollars,  and 
a  pair  of  boots  for  11  dollars;  what  did  they  all  cost  him? 

*  Ans.  95  dollars. 

8.  A  man  earns  45  dollars  a  month,  but  spends  26  dol- 
lars a  month ;  how  long  will  it  take  him  to  pay  for  5  aores 
of  land  at  38  dollars  an  acre  ?  Ans.  10  months. 

84 


PROMISCUOUS   PJIOBLEMS.  §115 


9.  A  farmer  has  tbree  tracts  of  land  :  the  first  coiatains 
244  acres,  the  second  twice  as  much  as  the  first,  and  the 
third  half  as  much  as  both  the  other  two  ;  how  many  acres 
has  he  in  all  ?  Ans.  1098  acres. 

10.  If  11  b(!eves  weigh  6017  pounds,  what  is  their  aver- 
age weight  ?  Ans.  547  pounds. 

n.  How  many  weeks  are  there  in  161  days? 

Ans.  23  weeks. 

12.  At  15  dollars  a  month,  how  long  could  you  hire  a 
man  to  work  for  225  dollars?  Ans.  15  months. 

13.  If  5280  feet  make  a  mile,  how  many  feet  are  there 
in  15  miles  ?  Ans.  79200  feet. 

14.  Willie  walked  2  miles  one  day,  4  miles  the  next,  and 
5  miles  the  next ;  how  many  feet  did  he  walk  in  all  ? 

Ans.  63360  feet. 

15.  If  the  multiplicand  is  529,  and  the  multiplier  is  19, 
what  is  the  product?  Ans.  9051. 

16.  If  the  product  is  36204,  and  the  multiplicand  is  1058, 
what  is  the  multiplier  ?  Ans.  38. 

17.  If  the  multiplier  is  41,  and  the  product  is  16441, 
what  is  the  multiplicand  ?  *  xVns.  401. 

18.  If  the  dividend  is  15170,  and  the  divisor  is  74,  what 
is  the  quotient  ?  Ans.  205. 

19.  If  the  divisor  is  95,  and  the  quotient  is  78,  what  is 
the  dividend  ?  Ans.  7410. 

20.  If  the  quotient  is  37,  and  tlie  dividend  is  6512,  what 
is  the  divisor  1  Ans.  176. 

21.  Mr.  Jones  gave  his  daughter  1200  dollars,  his  son 
500  dollars  more  than  her,  and  his  wife  twice  as  much  as 
both  of  them  together  ;  what  did  he  give  his  wife  ? 

Ans.  3400  dollars. 

22.  Mr.  Smith  contributed  75  dollars  to  Domestic  Mis- 
sions, 25  dollars  lees  than  that  to  Foreign  Missions,  and  to 

85 


§115  .       PRIMART*  ARITHMETIC. 


the  Bible  Cause  twice  as   much    as   to    Foreign    Missions ; 
what  did  he  give  to  all  three  ?  Ans.  225  dollars. 

23.  A  dealer  bought  6  barrels  of  apples  at  13  dollars  a 
Ijfirrel,  and  sold  2  barrels  at  17  dollars,  and  the  rest  at  15 
dollars  ,  what  did  he  gain  on  the  whole?     Ans.  16  doll9,rs. 

24.  I  bought  19  cords  of  wood  for  133  dollars  :  I  after- 
wards sold  7  cords  of  it  at  a  loss  of  2  dollars  a  cord,  and 
the  rest  at  a  profit  of  3  dollars  a  cprd ;  what  did  I  receive 
for  the  wood  1  Ans.  155  dollars. 

25.  On  a  journey  of  576  miles,  I  have  traveled  9  days  at 
32  miles  a  day ;  but  I  am  compelled  to  finish  the  journey 
in  8  more  days  ;  at  what  rate  pf;r  day  must  I  travel  ? 

Ans.  36  miles. 

26.  A  man  sold  one  neighbor  28  acres  of  land  for   252 

dollars,  and  an  other  19  acres  at  the  same  rate :    what  did 

.  *        ■   . 

the  second  neighbor  pay  him  ?  Ans.  171  dollars. 

27.  How  many  acres  of  land  at  17  dollars  an  acre  may 
be  bought  for  289  dollars  ?  Ans."  17  acres. 

28.  If  5  bricklayers  can  do  a  certain  work  in  27  days,  in 
how  many  days  ought  3  men  to  do  the  same  work  ? 

Ans.  45  days. 

29.  What  should  be  paid  for  9  yards  of  broadcloth  at  7 
dollars  a  yard,  1  vest  pattern  at  6  dcliars,  1  pair  of  boots  at 
15  dollars,  3  yards  of  cassimere  at  5  dollars,  1  silk  hat  at  5 
dollars,  6  linen  shirts  at|4  dollars,  and  4  handkerchiefs  at 
2  dollars  apiece  ?  Ans.  136  dollars. 

30.  A  housekeeper  bought  2  barrels  of  flour  at  10  dol- 
lars a  barrel,  10  bushels  of  corn-  at  1  dollar,  5  hundred 
pounds  of  pork  at  6  dollars  a  hundred,  2  kegs  of  lard  at  15 
dollars  a  keg,  and  1  sack  of  salt  at  4  dollars ;  what  did  he 
pay  fgr  all  ?  Ans.  94  dollars. 

31.  In  a  collecting  tour,  I  received  from  one  debtor  29 
dollars,  from  an  other  13  dollars  more  than  from  the  first, 

86 


PROMISCUOUS  PROBLEMS.  §116 

from  a  third  6  dollars  less  than  from  the  second,  and  from 
a  fourth  3  dollars  more  than  from  the  first  three ;  how 
much  did  I  collect  in  all  ?  Ans.  217  dollars. 

32.  The  divisor  is  32,  the  quotient  is  802,  the  remainder 
is  23;  what  is  the  dividend  ?  Ans.  9687. 

33.  The  remainder  is  33,  the  minuend  is  303  ;  what  is 
the  subtrahend  ?  Ans.  270. 

34.  The  multiplicand  is  304,  the  multiplier  is  43 ;  what 
is  the  product  ?  Ans.  13072. 

35.  The  dividend  is  1855,  the  divisor  is  53  ;  what  is  the 
quotient '(  Ans.  35. 

36.  The  prQduct  is  19278,  the  multiplicand  is  306  ;  what 
is  the  multiplier  1  Ans.  63. 

37.  The  subtrahend  is  370,  the  remainder  is  307 ;  what 
is  the  minuend  ?  Ans.  677. 

38.«  What  is  the  difference  between  twenty-seven  and 
twenty-seven  thousand  ?  Ans.  26973. 

39.  What  is  the  sum  of  twenty-seven  and  twenty-seven 
thousand  ?  Ans.  27027. 

40.  What  is  the  product  of  twenty-seven  and  twenty- 
seven  thousand  ?  Ans.  629000. 

41 .  What  is  the  quotient  of  twenty-seven  thousand  by 
twenty-seven  ?  .    Ans.  1000. 

42.  A  farmer  who  has  50  sheep,  buys  from  his  neighbor 
^  more  ;  he  then  sells  25  to  the  butcher ;  how  many  has 
he  left?  Ans.  75. 

43.  John  had  40  apples ;  he  gave  his  brother  10,  kept  10 
for  himself,  and  divided  the  remainder  equally  between  his 
two  sisters;  how  many  had  they  apiece  ?  Ans.  10. 

44.  A  gentleman  dying,  left  his  estate,  which  amounted 
to  25000  dollars,  to  his  son  and  two  daughters,  as  follows  : 
to  his  son  he  gave  13000  dollars,  and  to  his  two  daughters 


87 


§115  ■   PRIMARY   ARITHMETIC. 


the  remainder,  to  be  divided  equally  between  them ;    how 
much  apiece  had  the  daughters  ?  Ans.  6000  dollars. 

45.  A  merchant  bought  8200  barrels  of  flour;  he  then 
gold  3766  barrels ;  he  then  bought  5000  barrels ;  after  which 
he  sold  4879  barrels ;  how  many  barrels  of  flour  has  he  still 
on  hand  ?  Ans.  4565. 

46.  A  man  who  sets  out  on  a  journey,  intends  to  travel 
2450  miles;  how  far  must  he  go  every  day,  to  perform  the 
journey  in  50  days  ?  Ans.  49  miles. 

47.  A  grocer  bought  24  bags  of  cofl'ee,  containing  3000 
pounds,  and  sells  15  bags,  containing  1736  pounds;  how 
many  bags,  and  how  many  pounds,  has  he  remaining  ? 

Ans.  9  bags,  1264  pounds. 

48.  Supposing  a  man  to  receive  in  a  year  2920  dollars, 
how  much  a  day  is  his  income  at  that  rate;  and  supposing 
that  his  expenses  for  the  whole  year  amount  to  1769  dol- 
lars, how  much  will  he  save  in  a  year? 

Ans.  His  income  will  be  8  dollars  a  day,  and 
he  will  save  1151  dollars  a  year. 

88 


TABLES.    . 

KELATIONS  OF  CONCRETE  NUMBERS. 

§116.  The  relations  of  the  concrete  numl^ers  in  most 
general  use  are  given  the  following  tables. 

§  117.         XJiaited  States  IMoney. 

10  mills,  m. 
10  cents 
10  dimes 
10  dollars 

"  Though  there  are  five  denominations  given  in  this  table, 
yet  only  two  of  them  are  in  general  use,  namely,  dollars 
and  cents. 

Thuf!,  instead  of  2E.  $7,  4d.  5ct.,  we  usually  say  $27, 
45ct.,  or,  as  it  is  generally  written'  $27.45,  the  cents  being 
simply  separated  from  the  dollars  l^y  a  period, 

1.  In  5  cents,  how  many  mills  1 

2.  In  6  dimes,  how  many  cents  ? 

3.  In  4  dollars,  how  many  cents?  "  - 

4.  In  3  Eagles,  how  many  dollars? 

§  Ho.      English,  or  Sterling  ]Money- 


make 

1  cent. 

ct. 

i( 

1  dime 

d. 

<( 

1  dollar 

$ 

(( 

1  Eagle 

E. 

4  farthings,  qr. 

make 

1  penny, 

d. 

12  pence 

a 

1  shilling, 

s. 

20  shillings 

<( 

1  pound, 

£ 

Also,  5  shillings 

a 

1  crown, 

21  shillings 

(( 

1  guinea. 

89 

§119  PRIMARY   ARITHMETIC. 

1  pound  Sterling  is  worth  $4.84  by  a'law  of  tlie  United 
States. 

« 

1.  In  3  guineas,  how  many  shillings  ? 

2.  In  lOcrowns,  how  many  shillings? 

3.  In  £2,  how  many  pence  ?  .         • 

4.  In  3  shillings,  how  many  farthings  ? 

§  119.    ^iPrench.  ZMoney. 

10  centimes,  cent.  make     1  decime,       dec. 

'  10  decimes  '^         1  franc,  f.  • 

French  money  is  usually  counted  in  francs  and  centimes, 
which,  like  dollars  and  cents,  are  simply  separated  by  a 
period. 

Thus,  27.19f.  is  equal  to  27f.  Idee.  9cent. 

1  franc  is  worth  18ct.  6m.  United  States  currency. 

1.  How  many  decimes  m  5  francs  ? 

2.  How  many  centimes  in '5  francs'? 

3.  How  many  francs  in  60  decimes  ? 

4.  How  many  decimes  in  70  centimes?  • 

§120.      Troy  ^Weight.  ■ 

Used  for  weighing  gold,  silver,  jewels,  &c. 
24  grains,  gr.  make     1  pennyweight,     dwt. 

*20  pennyweights        "         1  ounce,  oz. 

12  ounces  "         1  poilnd,  lb. 

li  In  48  grainy,  how  many  pennyweights  ? 

2.  In  60  pennyweights,  how  many  ounces  ? 

3.  In  72  ounces,  how  many  pounds  ? 

4.  In  5  pounds,  how  many  pennyweights? 

5.  In  80  pennyweights,  how  many  ounces  ? 

6.  In  4  pounds,  how  many  grains? 

'90 


TABLES.  §123 

J  i-^i.      _A.potb.ecaries'  "Weiglit. 

Used  in  mixing  medicines. 

20  grains,  gr.  make     1  scruple,  sc.  or  9 

3  scruples                    "         1  dram,  dr.  or  3 
8  drams     ■               .  "         1  ounce,  oz.  or  ^ 

12  ounces  *•'         1  pound,      lb.  or  flb. 

The  pound  Apothecaries'  is  the  same  as  the  pound  Troy. 

1.  In  40  grains,  h#w  many  scruples? 

2.  In  40  drams,  how  many  scruples  ? 

3.  In  16  drams,  how  many  ounces? 

4.  In  16  pounds,  how  many  ounces  ? 

S  1~"C.      .A-voirdixpois  Weight. 

Used  for  weighing  all   articles  except   those   men-. 
tioned  in  §§120  and  121. 

16  drams,  dr.           make  1  ounce,                    oz. 

16  ounces                     "  1  pound,                   lb. 

25  pounds                    ''  1  quarter,                 qr. 

4  quarters                 "  1  hundredweight,  cwt. 
20  hundredweight     ''  1  ton,                          T. 

1.  H|?w  many  ounces  in  4  pounds  ?  • 

2.  How  many  pounds  in  3  quarters  ?  • 

3.  How  many  tons  in  40  hundredweight  ? 

4.  What  will  3  lb.  of  Indigo  cost,  at  25  cents  an  ounce  ? 

S  1^0.      Long  IMeasure  5    or.  Linear  Mieasure. 

Used  in  measuring  lines,  or  distances. 


12  inches,  in. 

make 

1  foot. 

ft. 

3  feet 

11 

1  yard. 

yd. 

5i  yards 

(( 

1  rod. 

rd. 

40  rods 

a 

1  furlong, 

fur. 

8  furlongs 

•11 

1  mile 

mi. 

91 

§124  PRIMARY   AEITHMETIC. 


1.  In  6  feet,  how  maii}^  inches? 

2.  In  3  yards,  how  many  feet  ? 

3.  In  3  yardf?,  how  man}?^  inches  ? 

Used  for  measuring  surfaces  of  land,  painting,  plas- 
tering, paving,  &c. 

144  square  inches,  sq.  in.  make  1  square  foot,    b{,|.,ft. 

9  square  feet  *•  1  square  yard,  sq.  yd. 

30i  square  jards  "  ?  perch,  P. 

40  perches  ''  1  rood,    .  R. 

4  roods  "  1  acre,  A. 

640  acres  ''  1  square  mile,  sq.  mi. 

1.  How  many  square  inches  in  8  square  feet  ? 

2.  How  many  square  yards  in  27  square  feet  ? 

3.  How  many  perches  in  16  roods  ? 

§  120.       Cnbic  ]VIea.so.re. 

Used  for  measuring  the  contents  of  solids. 
1728  cubic  inches,  cu.  in.     make     1  cubic  foot,     cu.  ft. 
27  cubic  feet  '^^         1  cubic  yard,  cu.  yd. 

1.  In  2  cubic  yards,  how  many  cubic  feet  1 

2.  In- 1  cubic  yarfli,  how  many  cubic  inches  1        • 
8.  In  54  cVibic  feet,  how  many  cubic  yards  ? 

§  126.      x>ry  Mleasxire. 

Used  for  measuring  grain,  fruits,  vegetables,  salt,  &c. 


2  pints,  pt. 

make 

1  quart,           qt. 

4  quarts 

a 

1  gallon,        gal. 

2  gallons 

a 

1  peck,           pk. 

4  pecks 

a 

1  bushel,        bu. 

'Also,     5 

bu 

shels 

a 

1  barrel,  of  corn. 

8 

bu 

shels 

a 

1  quarter. 

36 

bu 

shels 

a 

1  chaldron, 

92 

TABLES. 


•  , 


§128 


1.  In  4  barrels  of  corn,  how  many  bushels  ? 

2.  In  20  bushels,  how  many  pecks  ? 

3.  In  80  pecks,  how  many  gallons? 

4.  In  5  gallons,,  how  many  pints  ?         * 
H27. 


Liquid  IMeasure;    or.  Wine  Mieasixre. 

Used   in  measuring  liquids;    as,   molasses,   spirits, 
wiiie,  water,  &c. 

-t  gills,  gi.  make 

2  pints 
4  quarts 
31^  gallons 
2  barrels,  or  63  gallons  '^ 
'-  hogsheads 
2  pipes 

Also,  42  gaHons 
2  tierces 


a 
a 

iC 

a 

ii 
i( 


1  pint, 

1  quarf, 

1  gallon, 

1  barrel, 


pt. 

qt. 
gal. 
bbl. 


1  hogshead,      hhd. 
i  pipe,  pi. 

1  tun,  tun. 

1  tierce, 
1   puncheon. 


1 .   What  will  3  quarts  of  wine  cost,  at  2  dollars  a  pint  ? 


t 


In  2  hogsheads,  how  many  gallons?. 
In  3  gallons,  how  many  pints  ? 
■a  1  gallon,  how  many  gills  ? 


V!*'  seconds,  sec. 
fiO  minutes 
-  I  hours 
365  j   <'ays 
M'  years 
V''  deuades 
Alwo,  7  days 

30  or  31  days 
12  months 


make     1  minute, 

1  hour, 

1  day, 

1  year, 

1  decade, 

1  century, 

1  week, 

1  month, 

1  year. 


u 
(< 
li 
(( 
li 
ii 
ii 
ii 


min. 
hr. 
da. 

dec. 

cent. 

wk. 

mo. 


•din^  to  the  table,  365^  days  make  a  year.    To  avoid 
tiio  aaticulty  arising  from  the  fraction,  we  reckon  three 
93 


§128 


Primary  arithmetic. 


years  of  365  days  each,  and  one  of  366  days.  This  long 
year  is  called  leap  year.  The  leap  years  are  those  whose 
numbers  are  exactly  divisible  by  4 ;  except  that  the  cen- 
tonniah  years  are -not  leap  years  unless  their  numbers  are 
exactly  divisible  by  400.  Thus,  1860  and  1848' were  leap 
years ;  but  1900  will  not  be  leap  year,  because  it  is  not 
divisible  by  400. 

The  year  is  also  divided  into  four  seasons;  Spring,  Sum- 
mer, Autumn,  and  Winter.  These  consist  of  the  following 
ufconths : —         * 


Spiking, 


3. 

March,  . 

Mar. 

has 

31 

days. 

4. 
5. 

April, 

May, 

Apr. 

May 

30 
31 

d 

6. 

June, 

Jun. 

30 

({ 

7. 
8. 

July, 
August, 

Jul.. 

Aug. 

31 
31 

li 
« 

9. 

10. 

September, 
October, 

Sept. 
Oct. 

30 
31 

a 
(I 

11. 

November, 

Nov. 

30 

a 

12. 

December, 

Dec. 

31 

a 

1. 
2. 

January, 
•February, 

Jan, 
Feb. 

31 

28 

(i 

SUJIMEE, 


Autumn. 


Winter, 


Thirty  days  have  September, 
April,  June  and  November; 
All  the  rest  have  thirty-one, 
Except  February  alone, 
•    .  Which  has  but  twenty-eight  in  fine, 
Till  leap  year  gives  it  twenty-nine. 

1.  How  many  days  are  there  in  the  three  Spring  months  ? 

2.  Is  1865  a  leap  year  or  not  ? 

3.  In  2  centuries,  how  many  decades  ? 

4.  In  50  years,  how  many  decades  ?  * 

94 


TABLES.  §1S0 

§129.     i>.A.i*id:3R,. 

24  sheets,  sh.  make     1  ({uirc,  qr. 

20  quires  "         1  ream,  rm. 

2  reams  "         1  >)ur-dle,        bdle. 

5  bundles  "         1  bale. 

1.  How  many  Blieets  of  paper  in  1  ream  ? 

2.  How  many  quires  in  5  reams  ? 

3.  How.  many  reams  in  40  quires  ? 

4.  How  many  sheets  in  40  quires? 

§  130.      i3XJOI>E;CI]M-A.lLiS. 

12  units  make     1 

1J&  dozen  "         1 

12  gross  "         1 

A'lso,  20  units  ''      ^1 

1.  In  1  gross,  how  many  units? 

2.  In  24  dozen,  how  many  gross  ? 

3.  In  1  great  gross,  how  many  units  ? 

4.  How  many  units  in  3  score  and  10? 

95 


dozen, 

doz 

gross, 

gr- 

great  gross, 

score. 

^"S. 


PART     I.— MENTAL. 


Addition, 


•5" 


Subtraction. 10 

Multiplication, 19 

Division, ; 27 

PAET^  II.—MENTAL. 

Notation  and  Addition,.'. 35 

Notation  and  Subtraction, 42 

Notation  and  Multiplication, ., 49 

Notation  and  Division, 5(^ 

PART     III.— WRITTEN. 

Notation, ,....,..  .CI 

Addition, ?'"> 

Subtraction, t^ S2 

Promiscuous  Problems, 90 

Multiplication, ,  91 

Division, . .  105 

Promiscuous  Problems, .-  115 

Tables.— Money, 117 

Weights,..-./.; 120 

Measures,.. 123 

Promiscuous, 1'3S 

98 


Si' 


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